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受欢迎的三角函数 >

cos(arctan(sqrt(3))-arcsin((sqrt(3))/2))

解答

cos (arctan (3) - arcsin (\frac{3}{2}))

解答

1

求解步骤

cos (arctan (3) - arcsin (\frac{3}{2}))

使用三角恒等式改写:

cos (arctan (3)) cos (arcsin (\frac{3}{2})) + sin (arctan (3)) sin (arcsin (\frac{3}{2}))

cos (arctan (3) - arcsin (\frac{3}{2}))

使用角差恒等式:

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

= cos (arctan (3)) cos (arcsin (\frac{3}{2})) + sin (arctan (3)) sin (arcsin (\frac{3}{2}))

= cos (arctan (3)) cos (arcsin (\frac{3}{2})) + sin (arctan (3)) sin (arcsin (\frac{3}{2}))

使用三角恒等式改写:

cos (arctan (3)) = \frac{1}{2}

cos (arctan (3))

使用三角恒等式改写:

cos (arctan (3)) = \frac{1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

利用以下特性:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= \frac{1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

= \frac{1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

化简

= \frac{1}{2}

使用三角恒等式改写:

cos (arcsin (\frac{3}{2})) = \frac{1}{2}

cos (arcsin (\frac{3}{2}))

使用三角恒等式改写:

cos (arcsin (\frac{3}{2})) = 1 - (\frac{3}{2})^{2}

利用以下特性:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{3}{2})^{2}

= 1 - (\frac{3}{2})^{2}

化简

= \frac{1}{2}

使用三角恒等式改写:

sin (arctan (3)) = \frac{3}{2}

sin (arctan (3))

使用三角恒等式改写:

sin (arctan (3)) = \frac{3 1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

利用以下特性:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{3 1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

= \frac{3 1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

化简

= \frac{3}{2}

使用三角恒等式改写:

sin (arcsin (\frac{3}{2})) = \frac{3}{2}

利用以下特性:

sin (arcsin (x)) = x

= \frac{3}{2}

= \frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2}

化简

\frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2} : 1

\frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

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

分式相乘:

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

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

数字相乘:

1 \cdot 1 = 1

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

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

\frac{3}{2} \cdot \frac{3}{2} = \frac{3}{4}

\frac{3}{2} \cdot \frac{3}{2}

分式相乘:

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

= \frac{3 3}{2 \cdot 2}

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{3}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{3}{4}

= \frac{1}{4} + \frac{3}{4}

使用法则

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

= \frac{1 + 3}{4}

数字相加:

1 + 3 = 4

= \frac{4}{4}

使用法则

\frac{a}{a} = 1

= 1

= 1

流行的例子

sin (2) (35)

3 \cdot cos (6 0^{\circ})

arccos((8.5)/(9.9))

arccos (\frac{8.5}{9.9})

csc(pi/2)+cot(pi/2)

csc (\frac{π}{2}) + cot (\frac{π}{2})

sin (\frac{5 π}{9})