Question

Question #41b0c

Answer 1

`x = 60°, 300°`

Explanation:

Based on the pythagorean identity:

`cos^2x+sin^2x=1`

If we solve for `sin^2x`, we get:

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

If we subsititute this value of `sin^2x` into the original equation we get:

`4(1-cos^2x) = 1+4cosx`

If we distribute and move everything to the right side we get:

`0=4cos^2x + 4cosx-3`

Now we can factor this:

`0 = (2cosx-1)(2cosx+3)`

Set both sides equal to 0 and solve:

`2cosx-1 = 0`
`cosx = 1/2`
`x = +-arccos(1/2)`
`x = 60°, -60° = 60°, 300°`

`2cosx + 3=0`
`cosx = -3/2`
`x = +-arccos(-3/2)`
`NRS`

`therefore x = 60°, 300°`