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人気のある三角関数 >

(1-tan^2(A))/(1+tan^2(A))=1

解

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1

解

A = πn

+1

度

A = 0^{\circ} + 18 0^{\circ} n

解答ステップ

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1

置換で解く

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1

仮定:

tan (A) = u

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

\frac{1 - u ^{2}}{1 + u ^{2}} = 1 : u = 0

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

以下で両辺を乗じる:

1 + u^{2}

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

以下で両辺を乗じる:

1 + u^{2}

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2}) = 1 \cdot (1 + u^{2})

簡素化

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2}) = 1 \cdot (1 + u^{2})

簡素化

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2}) : 1 - u^{2}

\frac{1 - u ^{2}}{1 + u ^{2}} (1 + u^{2})

分数を乗じる:

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

= \frac{( 1 - u ^{2} ) ( 1 + u ^{2} )}{1 + u ^{2}}

共通因数を約分する:

1 + u^{2}

= 1 - u^{2}

簡素化

1 \cdot (1 + u^{2}) : 1 + u^{2}

1 \cdot (1 + u^{2})

乗算:

1 \cdot (1 + u^{2}) = (1 + u^{2})

= (1 + u^{2})

括弧を削除する:

(a) = a

= 1 + u^{2}

1 - u^{2} = 1 + u^{2}

1 - u^{2} = 1 + u^{2}

1 - u^{2} = 1 + u^{2}

解く

1 - u^{2} = 1 + u^{2} : u = 0

1 - u^{2} = 1 + u^{2}

1

を右側に移動します

1 - u^{2} = 1 + u^{2}

両辺から

1

を引く

1 - u^{2} - 1 = 1 + u^{2} - 1

簡素化

- u^{2} = u^{2}

- u^{2} = u^{2}

u^{2}

を左側に移動します

- u^{2} = u^{2}

両辺から

u^{2}

を引く

- u^{2} - u^{2} = u^{2} - u^{2}

簡素化

- 2 u^{2} = 0

- 2 u^{2} = 0

以下で両辺を割る

- 2

- 2 u^{2} = 0

以下で両辺を割る

- 2

- 2 u^{2} = 0

以下で両辺を割る

- 2

\frac{- 2 u ^{2}}{- 2} = \frac{0}{- 2}

簡素化

u^{2} = 0

u^{2} = 0

規則を適用

x^{n} = 0 \Rightarrow x = 0

u = 0

u = 0

代用を戻す

u = tan (A)

tan (A) = 0

tan (A) = 0

tan (A) = 0 : A = πn

tan (A) = 0

以下の一般解

tan (A) = 0

tan (x)

πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

A = 0 + πn

A = 0 + πn

解く

A = 0 + πn : A = πn

A = 0 + πn

0 + πn = πn

A = πn

A = πn

すべての解を組み合わせる

A = πn

グラフ

人気の例

sin (2 x) - 0.8 = 0

tan(a)=sqrt(15/7),sin(a)

tan (a) = \frac{15}{7}, sin (a)

2cos^2(θ)+sin(θ)=2

2 cos^{2} (θ) + sin (θ) = 2

tanh^2(x)+5sech(x)-5=0

tanh^{2} (x) + 5 sech (x) - 5 = 0

solvefor a,P=cot^2(a)

so l v e f or a, P = cot^{2} (a)