Question

Find all solutions of the equation 4Sin²x + 2Cos²x = 3

Answer 1

Explanation:

Factor out 2

`2(2 \sin {}^(2) (x) + \cos {}^(2) (x) ) = 3`

`2 \sin {}^(2) (x) + \cos {}^(2) (x) = 1.5`

`2 \sin {}^(2) (x) + (1 - \sin {}^(2) (x) ) = 1.5`

`\sin {}^(2) (x) = 0.5`

`\sin(x) = (1)/( √(2) ) = ( √(2) )/(2)`

or

`\sin(x) = - ( √(2) )/(2)`

We get

`x = (\pi)/(4)`

`x = (3\pi)/(4)`

`x = (5\pi)/(4)`

`x = (7\pi)/(4)`