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受欢迎的代数 >

展开 cotan(2/11+24/7)

解答

展开

co tan (\frac{2}{11} + \frac{24}{7})

解答

tan (\frac{278}{77}) co

求解步骤

co tan (\frac{2}{11} + \frac{24}{7})

使用三角恒等式改写

= co \frac{- sin ( \frac{2}{11} ) cos ( \frac{24}{7} ) - cos ( \frac{2}{11} ) sin ( \frac{24}{7} )}{sin ( \frac{2}{11} ) sin ( \frac{24}{7} ) - cos ( \frac{2}{11} ) cos ( \frac{24}{7} )}

分式相乘:

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

= \frac{( - sin ( \frac{2}{11} ) cos ( \frac{24}{7} ) - cos ( \frac{2}{11} ) sin ( \frac{24}{7} ) ) co}{sin ( \frac{2}{11} ) sin ( \frac{24}{7} ) - cos ( \frac{2}{11} ) cos ( \frac{24}{7} )}

使用角和恒等式:

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

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

= \frac{( - sin ( \frac{2}{11} + \frac{24}{7} ) ) co}{sin ( \frac{2}{11} ) sin ( \frac{24}{7} ) - cos ( \frac{2}{11} ) cos ( \frac{24}{7} )}

去除括号:

(- a) = - a

= \frac{- sin ( \frac{2}{11} + \frac{24}{7} ) co}{sin ( \frac{2}{11} ) sin ( \frac{24}{7} ) - cos ( \frac{2}{11} ) cos ( \frac{24}{7} )}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{sin ( \frac{2}{11} + \frac{24}{7} ) co}{sin ( \frac{2}{11} ) sin ( \frac{24}{7} ) - cos ( \frac{2}{11} ) cos ( \frac{24}{7} )}

化简

\frac{2}{11} + \frac{24}{7} : \frac{278}{77}

= - \frac{sin ( \frac{278}{77} ) co}{sin ( \frac{2}{11} ) sin ( \frac{24}{7} ) - cos ( \frac{2}{11} ) cos ( \frac{24}{7} )}

使用角和恒等式:

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

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

= - \frac{sin ( \frac{278}{77} ) co}{- cos ( \frac{2}{11} + \frac{24}{7} )}

整理后得

= \frac{sin ( \frac{278}{77} ) co}{cos ( \frac{2}{11} + \frac{24}{7} )}

化简

\frac{2}{11} + \frac{24}{7} : \frac{278}{77}

= \frac{sin ( \frac{278}{77} ) co}{cos ( \frac{278}{77} )}

使用基本三角恒等式:

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

= co tan (\frac{278}{77})

流行的例子

展开 (f(x)(x^2+2x-1))/(x+3)

e x p an d \frac{f ( x ) ( x ^{2} + 2 x - 1 )}{x + 3}

化简 (z-1)*(z-4/5)

s im pl i f y (z - 1) \cdot (z - \frac{4}{5})

展开 11(8e+3f)

e x p an d 11 (8 e + 3 f)

展开-(sqrt(5)(12sqrt(22)-11sqrt(3)))/(66)

e x p an d - \frac{5 ( 12 22 - 11 3 )}{66}

展开 (x^2+4x+6)^5

e x p an d (x^{2} + 4 x + 6)^{5}