Question

Number of solutions of sin^2θ+3cosθ=3 in [-π,π] ?

Answer 1

One answer: t = 0

Explanation:

Replace in the equation `sin^2 t` by `(1 - cos^2 t)`:, then, solve the quadratic equation for cos t:
`1 - cos^2 t + 3cos t - 3 = 0`
`- cos^2 t + 3cos t - 2 = 0`
Sine a + b + c = 0, use shortcut. The 2 real roots are:
cos x = 1 and `cos x = c/a = 2` (rejected as > 1)
cos x = 1.
Unit circle gives --> t = 0, and `t = 2pi`
Inside the interval `(-pi, pi)`, there is only one answer:
t = 0
Check
t = 0 --> sin^2 t = 0 --> 3cos t = 3
sin^2 t + 3cos t = 0 + 3 = 3. Proved.