Question

Solve for all real values of x using the equation cos^2 x - sin^2 x = √3/2 ?

Answer 1

`x =2kpi +- (pi / 12)^c`

Explanation:

`cos^2x - sin^2x = sqrt3 / 2`

We know `cos^2 x - sin^2 x = cos (2x)`, identity.

`:. cos (2x) = sqrt3 / 2`

We also know, `cos (30) = sqrt3 / 2`

Hence, `cos (2x) = cos (30) = cos (pi/6)`

Therefore `2x = 30` or `x = 15^@`