Question

Solve 2 cosx - sin²x + 2 =0 for all values of x.

Answer 1

`2\cos x-\sin^2x+2=0`

`2\cos x-(1-\cos^2x)+2=0`

`\cos^2x+2\cos x+1=0`

`(\cos x+1)^2=0`

`\cos x+1=0`

`\cos x=-1`

`\implies x=\pi+2k\pi`

where
`k` is an integer.