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

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

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

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

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

Solution steps

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

Subtract

1 - 2 sin (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 0, sin (x) = 1

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

cos (x) = - 0.34

2 sin^{2} (x) = 3 sin (x) - 1

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

sin (4 x) + 1 = cos (4 x)

tan (x) = \frac{36}{28}

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