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

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

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

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

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

Solution steps

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

Subtract

1 - 2 sin (x)

from both sides

cos (2 x) - 1 + 2 sin (x) = 0

Rewrite using trig identities

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

Solve by substitution

sin (x) = 0, sin (x) = 1

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

- cos (A) - 11 = 2 cos (A) - 9

sin (θ - \frac{π}{3}) - 1 = 0

cos (5 x) = \frac{1}{2}

sin (θ) = \frac{3}{5} cos (θ)

cos (\frac{x}{3}) = 0

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