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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

1 - sin^{2} (x)

from both sides

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

Solve by substitution

cos (x) = 1, cos (x) = - 1

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

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

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

- sin (θ) + 2 sin^{2} (θ) = 0

- sec (x) + 2 sec (x) cos (x) = 0

2 tan (x) - 3 sin (x) = 0

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