Question

Which shows all the exact solutions of sin^2 x + 3cos x - 1 = 2?

Answer 1

x = 2k
`\pi` is the solution of this equation.

Explanation:

This question is related to trigonometric equations.

The given equation is,

`sin^(2) x + 3cos x - 1 = 2`

We have to find the solutions of this equation.

Put
`sin^(2)x  = 1 - cos^(2)x`

`1 - cos^(2)x` + 3cosx - 1 = 2

`cos^(2)x -3cosx+2` = 0

For this equation only cosx = 1 is possible solution.

Cosx = 1 happens when x is a multiple of 2
`\pi`

So x = 2k
`\pi` is the solution of this equation.