Question

Solve for x.
2*cos^2(x)=3*sin(x)

Answer 1

Write cos^2(x) as 1-sin^2(x). You will get a quadratic in sin(x). Solve for the roots and then for x based on valid roots.

Answer 2

start with
\[2(1-\sin^2(x))=3\sin(x)\] and then solve the quadratic equation

Answer 3

2 sin^2 + 3sin - 2 = 0.

Answer 4

The solution is then sin x = -2 or 1/2. Only 1/2 is valid for sin.

Answer 5

So, since sin x = 1/2, x = pi / 6.