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

The general solution for cos^2(x)=(1-sin(2x))/2 is x=(3pi)/8+(pin)/2

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

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

x = \frac{3 π}{8} + \frac{πn}{2}

Solution steps

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

Subtract

\frac{1 - sin ( 2 x )}{2}

from both sides

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

Simplify

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

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

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

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

Rewrite using trig identities

1 + tan (2 x) = 0

Move

1

to the right side

tan (2 x) = - 1

General solutions for

tan (2 x) = - 1

2 x = \frac{3 π}{4} + πn

Solve

2 x = \frac{3 π}{4} + πn : x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

t, A (- sin (wt + d) w) = 0

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

4 sin (2 θ) - 5 sin (θ) = 0

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

tan (\frac{2 x}{3}) - 1 = 0

What is the general solution for cos^2(x)=(1-sin(2x))/2 ?
The general solution for cos^2(x)=(1-sin(2x))/2 is x=(3pi)/8+(pin)/2