# How do you solve 3sin^(2)x - sinxcosx - 4cos^(2)x = 0 from [-pi, pi]?

3${y}^{2}$ - ysqrt (1 - ${y}^{2}$ ) - 4 (1 - ${y}^{2}$ ) = 0, y = sinx
$\implies$ 7${y}^{2}$ = ysqrt (1 - ${y}^{2}$ ) $\implies$ 7y = sqrt(1 - ${y}^{2}$ )
$\implies$ y = 1/5sqrt 2 $\implies$ x = ${\sin}^{-} 1$ (1/ 5 sqrt 2 )
Squaring 7y = sqrt(1 - ${y}^{2}$ ), we get 49 ${y}^{2}$ = 1 - ${y}^{2}$ $\implies$
50 ${y}^{2}$ = 1 $\implies$ ${y}^{2}$ = 1/50 $\implies$ y = 1/5sqrt 2 .