Question

3cos theta= 2 sin^2 theta. find the value of theta​

Answer 1

SOLUTION:

3 cosθ = 2 sin²θ

==> 3 cosθ = 2(1 - cos²θ)

==> 3 cosθ = 2 - 2 cos²θ

==> 3 cosθ + 2 cos²θ - 2 = 0

==> 2 cos²θ + 4 cosθ - cosθ - 2 = 0

==> 2 cosθ(cosθ + 2) - 1(cosθ + 2) = 0

==> (2 cosθ - 1)(cosθ + 2) = 0

==> 2 cos - 1 = 0 OR cosθ + 2 = 0

==> cosθ = 1/2 OR cosθ = -2

Answer can't be negative, so, 1/2 is the required root.

∴ cosθ = 1/2

==> θ = 60⁰

∴ Value of θ is 60⁰