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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

3 (sec (θ)) = 10

2 sin^{2} (3 x) - 1 = 0

4 sin^{3} (x) + 2 sin^{2} (x) = 2 sin (x) + 1

(tan (x) + 1)^{2} = 0

cos (2 x) + 3 = 5 cos (x)

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