展开 (cot(x)(sin(x)+tan(x)))/(csc(x)+cot(x))

解答

展开

\frac{cot ( x ) ( sin ( x ) + tan ( x ) )}{csc ( x ) + cot ( x )}

\frac{cos ( x ) + 1}{csc ( x ) + cot ( x )}

求解步骤

\frac{cot ( x ) ( sin ( x ) + tan ( x ) )}{csc ( x ) + cot ( x )}

乘开

cot (x) (sin (x) + tan (x)) : cot (x) sin (x) + cot (x) tan (x)

= \frac{cot ( x ) sin ( x ) + cot ( x ) tan ( x )}{csc ( x ) + cot ( x )}

使用基本三角恒等式:

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

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

化简

\frac{cos ( x )}{sin ( x )} sin (x) : cos (x)

= \frac{cos ( x ) + cot ( x ) tan ( x )}{csc ( x ) + cot ( x )}

使用基本三角恒等式:

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

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

使用基本三角恒等式:

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

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

\frac{cos ( x )}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )} = 1

= \frac{cos ( x ) + 1}{csc ( x ) + cot ( x )}

e x p an d lo g_{10} (3 9 x^{4})

e x p an d (x - \frac{6}{5} ln (6)) (x - \frac{6}{5} ln (6))

e x p an d (6 + 5) (6 + 1) (6 - 5) (6 - 1)

e x p an d lo g_{3} (y^{2} - 1)

e x p an d 2 (\frac{512 π}{3} - \frac{2048}{9})