What is expand (1-2a)/((sin(a)-cos(a))^2) ?

The solution to expand (1-2a)/((sin(a)-cos(a))^2) is (1-2a)/(-sin(2a)+1)

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expand (1-2a)/((sin(a)-cos(a))^2)

expand

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

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

Solution steps

\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 )}

Use the Pythagorean identity:

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

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

\frac{4 e ^{2 s} + s + 1}{e ^{2 s} ( s + 1 ) ( 4 s ^{2} + 8 )}

A e^{- B s} (s - 2) + C e^{- Ds} (s - 1)

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

\frac{- a + 2 c ^{2} + c + a c ^{2} + c ^{3} - a ^{2}}{c b ( a + c )}

\frac{x ^{3} + 2 x - 2}{( x ^{2} + 1 ) ^{2}}

What is expand (1-2a)/((sin(a)-cos(a))^2) ?
The solution to expand (1-2a)/((sin(a)-cos(a))^2) is (1-2a)/(-sin(2a)+1)