Question

Cos^2x-sin^2x=sqrt 3/2

Answer 1

`\cos^2x-\sin^2x=\cos2x=\frac{\sqrt3}2`

In the interval
`[0,2\pi)`,
`\cos x` takes on the value of
`\frac{\sqrt3}2` when
`x=\pm\frac\pi3`. In general, this happens for
`x=\pm\frac\pi3+2n\pi` where
`n` is any integer.

So, the solutions to this equation satisfy


`2x=\pm\frac\pi3+2n\pi`

or, dividing by 2,


`x=\pm\frac\pi6+n\pi`

for all integers
`n`.