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

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 (θ) - sin (θ) = 0

cos (x + \frac{π}{6}) = sin (x)

sin (θ) = - \frac{1}{5}

5 cot (x) - 5 = 0

2 - \frac{1}{2} sin (3 x + 330) = \frac{8 - 3}{4}

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