Question

Find the possible values of sin x, if $8\sin x-\cos x=4$ .

Answer 1

$3\sin x-\cos 44=4\Rightarrow 3\sin A-4=\cos x$

${\sin }^{2}x+(B\sin \times -4{)}^2=1$

${\sin }^{2}x+64{\sin }^{2}x-64\sin x+16=1$

$65{\sin }^{2}x-64\sin x+15=0$

$\sin x=\frac{3}{5}\sin x=\frac{5}{13}$

$\sin x=\{\frac{3}{5},\frac{5}{13}\}$