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Hello Kristen Jacobs, 2 + 2 sin @ = 4(1 -sin^2 @)
So cancelling 2 through out, we have 1 + sin@ = 2 - 2 sin^2@
OR 2 sin^2@ + sin@ -1 = 0
(2 sin@ - 1 )(sin@ + 1) = 0
So two options, sin@ = 1/2 or sin@ = -1
So @ = pi/6 or @ = 3 pi/2
2 + 2sin θ = 4cos² θ = 4(1 - sin² θ)
4sin² θ + 2sin θ - 2 = 0
2(2sin² θ + sin θ - 1)
2(2sin θ -1)(sin θ + 1) = 0
Above are the factors you wanted. if you wish, you can now derive values for θ from 2sin θ = 1 and sin θ = -1
Comments
Hello Kristen Jacobs, 2 + 2 sin @ = 4(1 -sin^2 @)
So cancelling 2 through out, we have 1 + sin@ = 2 - 2 sin^2@
OR 2 sin^2@ + sin@ -1 = 0
(2 sin@ - 1 )(sin@ + 1) = 0
So two options, sin@ = 1/2 or sin@ = -1
So @ = pi/6 or @ = 3 pi/2
2 + 2sin θ = 4cos² θ = 4(1 - sin² θ)
4sin² θ + 2sin θ - 2 = 0
2(2sin² θ + sin θ - 1)
2(2sin θ -1)(sin θ + 1) = 0
Above are the factors you wanted. if you wish, you can now derive values for θ from 2sin θ = 1 and sin θ = -1