What is expand (cos(x)+isin(x))/((cos(a)-sin(a)i)^2) ?

The solution to expand (cos(x)+isin(x))/((cos(a)-sin(a)i)^2) is cos(x+2a)+isin(x+2a)

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expand (cos(x)+isin(x))/((cos(a)-sin(a)i)^2)

expand

\frac{cos ( x ) + i sin ( x )}{( cos ( a ) - sin ( a ) i ) ^{2}}

cos (x + 2 a) + i sin (x + 2 a)

Solution steps

\frac{cos ( x ) + i sin ( x )}{( cos ( a ) - sin ( a ) i ) ^{2}}

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

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

Use the Double Angle identity:

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

= \frac{cos ( x ) + i sin ( x )}{- i sin ( 2 a ) + cos ( 2 a )}

Rationalize

\frac{cos ( x ) + i sin ( x )}{- i sin ( 2 a ) + cos ( 2 a )} : cos (x + 2 a) + i sin (x + 2 a)

= cos (x + 2 a) + i sin (x + 2 a)

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

(s + 3)^{2}

\frac{x}{( x - 1 ) ( x - 2 )}

(x - 5) (x + 4 + 3)

(2 sin (π x) + 2 sin (2 π x))^{2}

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