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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

\frac{1 - cos ^{2} ( x )}{2}

from both sides

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

Simplify

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

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

sin^{2} (x) = 0

Apply rule

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

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) = - \frac{1}{2}, 0 < x < 2 π

cot (θ) = cos (θ)

3 sin^{2} (θ) - cos (θ) + 1 = 0

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

3 csc^{3} (x) - 4 csc (x) = 0

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