Question

Find all solutions of the equation in the interval [0, 2π).

Answer 1

x=0

Explanation:

`4 \cos(x) = - \sin {}^(2) (x) + 1`

`4 \cos(x) = 1 - \sin {}^(2) (x)`

`4 \cos(x) = \cos {}^(2) (x)`

`4 \cos(x) - \cos {}^(2) (x) = 0`

`\cos(x) (4 - \cos(x) ) = 0`

`\cos(x) = 0`

`x = 0`

`4 - \cos(x) = 0`

`\cos(x) = 4`

There is no solution here because cosine is undefined it the range is not between -1 and 1 so the only answer is 0.