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

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

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

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

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

Solution steps

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

Subtract

1 - 2 cos^{2} (x)

from both sides

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

Rewrite using trig identities

cos^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

cos (x) = 0

General solutions for

cos (x) = 0

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

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

3 + 8 cos (2 θ) = - 1

- 4 cos^{2} (x) + 6 cos (x) = 2

sec (θ) = - \frac{4}{3}

tan (2 x) = tan (201 8^{\circ})

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