What is the general solution for cos^2(x)=(1+sin(x))(1-cos(x)) ?

The general solution for cos^2(x)=(1+sin(x))(1-cos(x)) is x=(3pi)/2+2pin,x= pi/4+pin

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cos^2(x)=(1+sin(x))(1-cos(x))

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

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

(1 + sin (x)) (1 - cos (x))

from both sides

cos^{2} (x) - (1 + sin (x)) (1 - cos (x)) = 0

Rewrite using trig identities

cos (x) - sin (x) - sin^{2} (x) + cos (x) sin (x) = 0

Factor

cos (x) - sin (x) - sin^{2} (x) + cos (x) sin (x) : (1 + sin (x)) (cos (x) - sin (x))

(1 + sin (x)) (cos (x) - sin (x)) = 0

Solving each part separately

1 + sin (x) = 0 or cos (x) - sin (x) = 0

1 + sin (x) = 0 : x = \frac{3 π}{2} + 2 πn

cos (x) - sin (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

tan (x) = 1, - π < x \leq π

\frac{1}{2 cos ^{2} ( x - 1 )} = \frac{1 + tan ^{2} ( x )}{2 sec ^{2} ( x )}

sin (2 x) - 2 cos (2 x) = 0

tan (x) = \frac{87.092}{86.676}

csc (x) = - \frac{3}{2}

What is the general solution for cos^2(x)=(1+sin(x))(1-cos(x)) ?
The general solution for cos^2(x)=(1+sin(x))(1-cos(x)) is x=(3pi)/2+2pin,x= pi/4+pin