math(Trigonometry)
posted by aaa .
2cos^2 theta + 5 sin theta  4 = 0

2(1sin^2) + 5sin  4 = 0
2sin^2  5sin + 2 = 0
(2sin1)(sin2) = 0
sin = 1/2 or 2
... 
can give me a further and detail explanation where did the theta on the 5 and the formula on changing the cos theta.

you know that cos^2 = 1sin^2
the rest is just algebra I
I dropped the thetas just for ease of typing.
Naturally, sin can never be 2, so that's a nonsolution, even though it does satisfy the original equation.