What is the general solution for cos(x)= 1/4-sin^2(x) ?

The general solution for cos(x)= 1/4-sin^2(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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cos(x)= 1/4-sin^2(x)

cos (x) = \frac{1}{4} - sin^{2} (x)

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

Solution steps

cos (x) = \frac{1}{4} - sin^{2} (x)

Subtract

\frac{1}{4} - sin^{2} (x)

from both sides

cos (x) - \frac{1}{4} + sin^{2} (x) = 0

Simplify

cos (x) - \frac{1}{4} + sin^{2} (x) : \frac{4 cos ( x ) - 1 + 4 sin ^{2} ( x )}{4}

\frac{4 cos ( x ) - 1 + 4 sin ^{2} ( x )}{4} = 0

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

4 cos (x) - 1 + 4 sin^{2} (x) = 0

Rewrite using trig identities

3 + 4 cos (x) - 4 cos^{2} (x) = 0

Solve by substitution

cos (x) = - \frac{1}{2}, cos (x) = \frac{3}{2}

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = \frac{3}{2} :

No Solution

Combine all the solutions

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

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

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

sin (b) = \frac{3}{5}

cos (4 + x) = 0.45

(tan (θ) - 2) (16 sin^{2} (θ) - 1) = 0

What is the general solution for cos(x)= 1/4-sin^2(x) ?
The general solution for cos(x)= 1/4-sin^2(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin