Question

Solve the equation sin^2x=3Cos^2X.

I would love to graduate...so thanks in advance!

Answer 1

240°

Explanation:

`sin^2x=3cos^2x \\ \\ sin^2x=3(1 - sin^2x )\\ \\ sin^2x=3 - 3sin^2x \\ \\ sin^2x + 3sin^2x=3 \\ \\ 4sin^2x=3 \\ \\ sin^2x= (3)/(4) \\ \\ sinx= \sqrt{ (3)/(4) } \\ \\ sinx= ( √(3) )/(2) \\ \\ sinx= sin \: 60 \degree \\ \\ in \: the \: second \: quadrant \\ sinx= sin \: (180 \degree - 60 \degree ) = sin \: 120 \degree \\ \\ in \: the \: third \: quadrant \\ sin x= sin \: (180 \degree + 60) \degree = sin \: 240 \degree`