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인기 있는 삼각법 >

cos^2(45-a)-sin^2(45-a)=sin^2(a)

해법

cos^{2} (4 5^{\circ} - a) - sin^{2} (4 5^{\circ} - a) = sin^{2} (a)

해법

a = 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n, a = 1.10714 \dots + 18 0^{\circ} n

+1

라디안

a = 0 + 2 πn, a = π + 2 πn, a = 1.10714 \dots + πn

솔루션 단계

cos^{2} (4 5^{\circ} - a) - sin^{2} (4 5^{\circ} - a) = sin^{2} (a)

삼각성을 사용하여 다시 쓰기

cos^{2} (4 5^{\circ} - a) - sin^{2} (4 5^{\circ} - a) = sin^{2} (a)

삼각성을 사용하여 다시 쓰기

sin (4 5^{\circ} - a)

각도 차이 식별 사용:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (4 5^{\circ}) cos (a) - cos (4 5^{\circ}) sin (a)

sin (4 5^{\circ}) cos (a) - cos (4 5^{\circ}) sin (a)

단순화하세요:

\frac{2 cos ( a ) - 2 sin ( a )}{2}

sin (4 5^{\circ}) cos (a) - cos (4 5^{\circ}) sin (a)

sin (4 5^{\circ}) cos (a) = \frac{2 cos ( a )}{2}

sin (4 5^{\circ}) cos (a)

sin (4 5^{\circ})

단순화하세요:

\frac{2}{2}

sin (4 5^{\circ})

다음과 같은 사소한 아이덴티티 사용:

sin (4 5^{\circ}) = \frac{2}{2}

sin (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2} cos (a)

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 cos ( a )}{2}

cos (4 5^{\circ}) sin (a) = \frac{2 sin ( a )}{2}

cos (4 5^{\circ}) sin (a)

cos (4 5^{\circ})

단순화하세요:

\frac{2}{2}

cos (4 5^{\circ})

다음과 같은 사소한 아이덴티티 사용:

cos (4 5^{\circ}) = \frac{2}{2}

cos (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2} sin (a)

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( a )}{2}

= \frac{2 cos ( a )}{2} - \frac{2 sin ( a )}{2}

규칙 적용

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 cos ( a ) - 2 sin ( a )}{2}

= \frac{2 cos ( a ) - 2 sin ( a )}{2}

각도 차이 식별 사용:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (4 5^{\circ}) cos (a) + sin (4 5^{\circ}) sin (a)

cos (4 5^{\circ}) cos (a) + sin (4 5^{\circ}) sin (a)

단순화하세요:

\frac{2 cos ( a ) + 2 sin ( a )}{2}

cos (4 5^{\circ}) cos (a) + sin (4 5^{\circ}) sin (a)

cos (4 5^{\circ}) cos (a) = \frac{2 cos ( a )}{2}

cos (4 5^{\circ}) cos (a)

cos (4 5^{\circ})

단순화하세요:

\frac{2}{2}

cos (4 5^{\circ})

다음과 같은 사소한 아이덴티티 사용:

cos (4 5^{\circ}) = \frac{2}{2}

cos (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2} cos (a)

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 cos ( a )}{2}

sin (4 5^{\circ}) sin (a) = \frac{2 sin ( a )}{2}

sin (4 5^{\circ}) sin (a)

sin (4 5^{\circ})

단순화하세요:

\frac{2}{2}

sin (4 5^{\circ})

다음과 같은 사소한 아이덴티티 사용:

sin (4 5^{\circ}) = \frac{2}{2}

sin (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2} sin (a)

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( a )}{2}

= \frac{2 cos ( a )}{2} + \frac{2 sin ( a )}{2}

규칙 적용

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 cos ( a ) + 2 sin ( a )}{2}

= \frac{2 cos ( a ) + 2 sin ( a )}{2}

(\frac{2 cos ( a ) + 2 sin ( a )}{2})^{2} - (\frac{2 cos ( a ) - 2 sin ( a )}{2})^{2} = sin^{2} (a)

(\frac{2 cos ( a ) + 2 sin ( a )}{2})^{2} - (\frac{2 cos ( a ) - 2 sin ( a )}{2})^{2}

단순화하세요:

2 cos (a) sin (a)

(\frac{2 cos ( a ) + 2 sin ( a )}{2})^{2} - (\frac{2 cos ( a ) - 2 sin ( a )}{2})^{2}

(\frac{2 cos ( a ) + 2 sin ( a )}{2})^{2} = \frac{( cos ( a ) + sin ( a ) ) ^{2}}{2}

(\frac{2 cos ( a ) + 2 sin ( a )}{2})^{2}

\frac{2 cos ( a ) + 2 sin ( a )}{2} = \frac{cos ( a ) + sin ( a )}{2}

\frac{2 cos ( a ) + 2 sin ( a )}{2}

공통 용어를 추출하다

2

= \frac{2 ( cos ( a ) + sin ( a ) )}{2}

\frac{2 ( cos ( a ) + sin ( a ) )}{2}

취소하다 :

\frac{cos ( a ) + sin ( a )}{2}

\frac{2 ( cos ( a ) + sin ( a ) )}{2}

급진적인 규칙 적용:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} ( cos ( a ) + sin ( a ) )}{2}

지수 규칙 적용:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{cos ( a ) + sin ( a )}{2 ^{1 - \frac{1}{2}}}

숫자를 빼세요:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{cos ( a ) + sin ( a )}{2 ^{\frac{1}{2}}}

급진적인 규칙 적용:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= \frac{cos ( a ) + sin ( a )}{2}

= \frac{cos ( a ) + sin ( a )}{2}

= (\frac{cos ( a ) + sin ( a )}{2})^{2}

지수 규칙 적용:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( cos ( a ) + sin ( a ) ) ^{2}}{( 2 ) ^{2}}

(2)^{2} : 2

급진적인 규칙 적용:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

지수 규칙 적용:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

공통 요인 취소:

2

= 1

= 2

= \frac{( cos ( a ) + sin ( a ) ) ^{2}}{2}

(\frac{2 cos ( a ) - 2 sin ( a )}{2})^{2} = \frac{( cos ( a ) - sin ( a ) ) ^{2}}{2}

(\frac{2 cos ( a ) - 2 sin ( a )}{2})^{2}

\frac{2 cos ( a ) - 2 sin ( a )}{2} = \frac{cos ( a ) - sin ( a )}{2}

\frac{2 cos ( a ) - 2 sin ( a )}{2}

공통 용어를 추출하다

2

= \frac{2 ( cos ( a ) - sin ( a ) )}{2}

\frac{2 ( cos ( a ) - sin ( a ) )}{2}

취소하다 :

\frac{cos ( a ) - sin ( a )}{2}

\frac{2 ( cos ( a ) - sin ( a ) )}{2}

급진적인 규칙 적용:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} ( cos ( a ) - sin ( a ) )}{2}

지수 규칙 적용:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{cos ( a ) - sin ( a )}{2 ^{1 - \frac{1}{2}}}

숫자를 빼세요:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{cos ( a ) - sin ( a )}{2 ^{\frac{1}{2}}}

급진적인 규칙 적용:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

= \frac{cos ( a ) - sin ( a )}{2}

= \frac{cos ( a ) - sin ( a )}{2}

= (\frac{cos ( a ) - sin ( a )}{2})^{2}

지수 규칙 적용:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( cos ( a ) - sin ( a ) ) ^{2}}{( 2 ) ^{2}}

(2)^{2} : 2

급진적인 규칙 적용:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

지수 규칙 적용:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

다중 분수:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

공통 요인 취소:

2

= 1

= 2

= \frac{( cos ( a ) - sin ( a ) ) ^{2}}{2}

= \frac{( cos ( a ) + sin ( a ) ) ^{2}}{2} - \frac{( cos ( a ) - sin ( a ) ) ^{2}}{2}

규칙 적용

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{( cos ( a ) + sin ( a ) ) ^{2} - ( cos ( a ) - sin ( a ) ) ^{2}}{2}

(cos (a) + sin (a))^{2} - (cos (a) - sin (a))^{2}

확대한다:

4 cos (a) sin (a)

(cos (a) + sin (a))^{2} - (cos (a) - sin (a))^{2}

(cos (a) + sin (a))^{2} : cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a)

완벽한 정사각형 공식 적용:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = cos (a), b = sin (a)

= cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a)

= cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a) - (cos (a) - sin (a))^{2}

(cos (a) - sin (a))^{2} : cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a)

완벽한 정사각형 공식 적용:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = cos (a), b = sin (a)

= cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a)

= cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a) - (cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a))

- (cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a)) : - cos^{2} (a) + 2 cos (a) sin (a) - sin^{2} (a)

- (cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a))

괄호 배포

= - (cos^{2} (a)) - (- 2 cos (a) sin (a)) - (sin^{2} (a))

마이너스 플러스 규칙 적용

- (- a) = a, - (a) = - a

= - cos^{2} (a) + 2 cos (a) sin (a) - sin^{2} (a)

= cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a) - cos^{2} (a) + 2 cos (a) sin (a) - sin^{2} (a)

cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a) - cos^{2} (a) + 2 cos (a) sin (a) - sin^{2} (a)

단순화하세요:

4 cos (a) sin (a)

cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a) - cos^{2} (a) + 2 cos (a) sin (a) - sin^{2} (a)

유사 요소 추가:

2 cos (a) sin (a) + 2 cos (a) sin (a) = 4 cos (a) sin (a)

= cos^{2} (a) + 4 cos (a) sin (a) + sin^{2} (a) - cos^{2} (a) - sin^{2} (a)

유사 요소 추가:

cos^{2} (a) - cos^{2} (a) = 0

= 4 cos (a) sin (a) + sin^{2} (a) - sin^{2} (a)

유사 요소 추가:

sin^{2} (a) - sin^{2} (a) = 0

= 4 cos (a) sin (a)

= 4 cos (a) sin (a)

= \frac{4 cos ( a ) sin ( a )}{2}

숫자를 나눕니다:

\frac{4}{2} = 2

= 2 cos (a) sin (a)

2 cos (a) sin (a) = sin^{2} (a)

2 cos (a) sin (a) = sin^{2} (a)

빼다

sin^{2} (a)

양쪽에서

2 cos (a) sin (a) - sin^{2} (a) = 0

2 cos (a) sin (a) - sin^{2} (a)

요인:

sin (a) (2 cos (a) - sin (a))

2 cos (a) sin (a) - sin^{2} (a)

지수 규칙 적용:

a^{b + c} = a^{b} a^{c}

sin^{2} (a) = sin (a) sin (a)

= 2 sin (a) cos (a) - sin (a) sin (a)

공통 용어를 추출하다

sin (a)

= sin (a) (2 cos (a) - sin (a))

sin (a) (2 cos (a) - sin (a)) = 0

각 부분을 개별적으로 해결

sin (a) = 0 or 2 cos (a) - sin (a) = 0

sin (a) = 0 : a = 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

sin (a) = 0

일반 솔루션

sin (a) = 0

sin (x)

주기율표

36 0^{\circ} n

주기:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

a = 0 + 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

a = 0 + 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

a = 0 + 36 0^{\circ} n

해결 :

a = 36 0^{\circ} n

a = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

a = 36 0^{\circ} n

a = 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

2 cos (a) - sin (a) = 0 : a = arctan (2) + 18 0^{\circ} n

2 cos (a) - sin (a) = 0

삼각성을 사용하여 다시 쓰기

2 cos (a) - sin (a) = 0

cos (a), cos (a) \neq = 0

양쪽을 다음으로 나눕니다

\frac{2 cos ( a ) - sin ( a )}{cos ( a )} = \frac{0}{cos ( a )}

단순화

2 - \frac{sin ( a )}{cos ( a )} = 0

기본 삼각형 항등식 사용:

\frac{sin ( x )}{cos ( x )} = tan (x)

2 - tan (a) = 0

2 - tan (a) = 0

2

를 오른쪽으로 이동

2 - tan (a) = 0

빼다

2

양쪽에서

2 - tan (a) - 2 = 0 - 2

단순화

- tan (a) = - 2

- tan (a) = - 2

양쪽을 다음으로 나눕니다

- 1

- tan (a) = - 2

양쪽을 다음으로 나눕니다

- 1

\frac{- tan ( a )}{- 1} = \frac{- 2}{- 1}

단순화

tan (a) = 2

tan (a) = 2

트리거 역속성 적용

tan (a) = 2

일반 솔루션

tan (a) = 2

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

a = arctan (2) + 18 0^{\circ} n

a = arctan (2) + 18 0^{\circ} n

모든 솔루션 결합

a = 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n, a = arctan (2) + 18 0^{\circ} n

해를 10진수 형식으로 표시

a = 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n, a = 1.10714 \dots + 18 0^{\circ} n

그래프

인기 있는 예

sin^2(2x)-cos^2(2x)=0

sin^{2} (2 x) - cos^{2} (2 x) = 0

cos^2(x)cos(x)=0

cos^{2} (x) cos (x) = 0

2 cos (x) = - 3

8sec(x)-3tan^2(x)=7

8 sec (x) - 3 tan^{2} (x) = 7

sin^2(6x)+sin^2(3x)=0

sin^{2} (6 x) + sin^{2} (3 x) = 0