Question

How do you solve `Sin^2 theta + cos theta = 2`?

Answer 1

No solution.

Explanation:

The maximum value of `sin^2theta` is 1 and the maximum value of
`costheta` is also 1. Since both functions cannot be 1 at the same time, the problem has no solution.

However, if you want to try, let's see:

`sin^2theta=1-cos^2theta`

So the expression transforms into:

`1-cos^2theta+costheta=2`

`cos^2theta-costheta+1=0`
(This is an expression o the type `ax^2+bx +c`)

`costheta=(1+-sqrt(1-4*1*1))/2`

`costheta=(1+-sqrt(-3))/2`

There is no solution.