Question

7cos^2a+ 3 sin^a = 4 solve

Answer 1

Assuming it's $7 * cos^{2}(a) + 3 * sin(a) = 4$

change cos(a) to sin(a) and lets say sin(a) = x

Then we have the quadratic equation $7 x^{2} - 3x - 4 = 0$

Solving it we get sin(a) = 0.9031, -0.260

Hope it will help you.

Answer 2

$7cos^2a+3sin^2a=4\\\\7(1-sin^2a)+3sin^2a=4\\\\7-7sin^2a+3sin^2a=4\\\\-4sin^2a=4-7\\\\-4sin^2a=-3\ \ \ \ |divide\ both\ sides\ by\ (-4)\\\\sin^2a=\frac{3}{4}\\\\sina=\sqrt\frac{3}{4}\\\\sina=\frac{\sqrt3}{2}\iff a=60^o$