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

The general solution for cos(x)=2sin^2(x)-1 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

Solution steps

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

Subtract

2 sin^{2} (x) - 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

sec^{2} (x) = 9

4 cos^{2} (x) - 3 = 0, 0 \leq x < 2 π

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

cos (4 x) = - 1

0.94 = 0.33 sin (x) + cos (x)

What is the general solution for cos(x)=2sin^2(x)-1 ?
The general solution for cos(x)=2sin^2(x)-1 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin