Question

How do ou solve `Sin^(2)[theta]=cos^(2)[theta]+1`?

Answer 1

`pi/2 and (3pi)/2`

Explanation:

Write f(t) in standard form:
`cos^2 t - sin^2 t + 1 = 0`.
Apply the trig identity; `cos 2a = cos^2 a - sin^2 a`, we get:
cos 2x + 1 = 0
cos 2x = -1 --> `2x= +- pi` --> `x = +- pi/2`
Answers for `(0, 2pi)`:
`pi/2 and (3pi)/2`