Question

If theta is a positive acute angles find theta when
2 sin^2 theta + 3 cos theta =3​

Answer 1

Theta = 0, 60 degrees.

Explanation:

2 sin^2 theta + 3 cos theta = 3​

Using the identity sin ^2 theta = 1 - cos^2 theta :

2(1 - cos^2 theta) + 3 cos theta = 3

2 - 2cos^2 theta) + 3 cos theta = 3

2 cos^2 theta - 3 cos theta + 3 - 2 = 0

2 cos^2 theta - 3 cos theta + 1 = 0

(2 cos theta - 1)(cos theta - 1) = 0

cos theta = 1/2 , cos theta = 1

Theta = 60 degrees or theta = 0