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

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

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

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

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

Solution steps

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

Subtract

2 sin^{2} (x)

from both sides

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

8 sec^{2} (\frac{x}{2}) = 4

6 cos^{2} (x) + cos (x) = 1

4 sin (x) + 3 cos (x) = 0

y, x = 2 sin (y)

2 sin (2 x) + 2 sin (x) = 1 + 2 cos (x)

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