展开 (sin(2x)(cot(x)-csc(x)))/(cot(x)+csc(x))

解答

展开

\frac{sin ( 2 x ) ( cot ( x ) - csc ( x ) )}{cot ( x ) + csc ( x )}

\frac{2 cos ^{2} ( x ) - sin ( 2 x ) csc ( x )}{cot ( x ) + csc ( x )}

求解步骤

\frac{sin ( 2 x ) ( cot ( x ) - csc ( x ) )}{cot ( x ) + csc ( x )}

乘开

sin (2 x) (cot (x) - csc (x)) : sin (2 x) cot (x) - sin (2 x) csc (x)

= \frac{sin ( 2 x ) cot ( x ) - sin ( 2 x ) csc ( x )}{cot ( x ) + csc ( x )}

sin (2 x) cot (x) = 2 cos^{2} (x)

= \frac{2 cos ^{2} ( x ) - sin ( 2 x ) csc ( x )}{cot ( x ) + csc ( x )}

e x p an d \frac{2 x ^{5} - x ^{4} + 3 x ^{3} - a x ^{2} + b x - c}{( x - 1 ) ^{3}}

e x p an d 5000 (- 0.125 e^{- 0.125 x} x + 1.75 e^{- 0.125 x})

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

e x p an d (α_{0} + α_{1} t + α_{2} t^{2})^{2} e^{t^{2}}

e x p an d \frac{- 18 x ^{2} - 18 x - 15}{( 3 x ^{2} + 3 x - 1 ) ^{2}}