Question

sin^2 theta -3sin theta + 2 = 0 then theta =?

Answer 1

I think the answer is 60

Answer 2

Given that sin²Ф - 3sinФ +2 = 0

Let sinФ = x

After putting values in given equation we get

x² -3x +2 = 0

x² - 2x - x +2 = 0 (middle term factorisation)

x (x -2) -1(x -2) = 0

(x - 2) (x - 1) = 0

x - 1 = 0              x - 2 = 0

x = 1                   x = 2 (not possible because value of sin is always -1 to 1)

∴ sin Ф = 1 (putting back x = sin Ф)

∴ sin Ф = sin 90° (∵ sin 90° =1)

∴ Ф = 90°