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

The general solution for sin^2(x)=2cos(x)+2 is x=pi+2pin

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

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

x = π + 2 πn

Solution steps

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

Subtract

2 cos (x) + 2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = - 1

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

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

y, sin (y) = x

sin (2 x) + 3 cos (x) = 0

tan (θ) = cot (θ)

sin (x) = 0.2

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