What is the general solution for sin^2(x)-2cos(x)-2=0 ?

The general solution for sin^2(x)-2cos(x)-2=0 is x=pi+2pin

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

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

x = π + 2 πn

Solution steps

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

\frac{1}{2} tan^{2} (x) = 1 - sec (x)

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

2 sec^{2} (x) + 3 (\frac{1}{cos ( x )}) = 2

cot^{2} (θ) - 3 = 0

tan (θ) = 2, sin (θ)

What is the general solution for sin^2(x)-2cos(x)-2=0 ?
The general solution for sin^2(x)-2cos(x)-2=0 is x=pi+2pin