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

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

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

expand

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

1

Solution steps

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

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

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

Use the Pythagorean identity:

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

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

Apply rule

\frac{a}{a} = 1

= 1

\frac{3 t ^{2} - 8 t + 5}{( t + 1 ) ^{4}}

(e^{x} + 2 x)^{4}

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

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

(x^{2} + 2 x + 1)^{6}

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