展开 (1-2a)/((sin(a)-cos(a))^2)

解答

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\frac{1 - 2 a}{( sin ( a ) - cos ( a ) ) ^{2}}

\frac{1 - 2 a}{- sin ( 2 a ) + 1}

求解步骤

\frac{1 - 2 a}{( sin ( a ) - cos ( a ) ) ^{2}}

(sin (a) - cos (a))^{2} = sin^{2} (a) - sin (2 a) + cos^{2} (a)

= \frac{1 - 2 a}{sin ^{2} ( a ) - sin ( 2 a ) + cos ^{2} ( a )}

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

= \frac{1 - 2 a}{- sin ( 2 a ) + 1}

e x p an d \frac{4 e ^{2 s} + s + 1}{e ^{2 s} ( s + 1 ) ( 4 s ^{2} + 8 )}

e x p an d A e^{- B s} (s - 2) + C e^{- Ds} (s - 1)

e x p an d e^{j (120 π \cdot t - \frac{π}{2})} + e^{- j (180 π \cdot t - \frac{π}{2})}

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

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