Question

sin2 x + 2sin x cos x -3cos2 x = 0.

Answer 1

$\sin(2x) + 2 \sin(x )\cos(x) - 3 \cos(2x) = 0$

$2 \tan(2x) - 3 = 0$

$2 \tan(2x) = 3$

$\tan(2x) = \frac{3}{2}$

$2x = \arctan( \frac{3}{2} ) + \pi \: n$

$x = \frac{ \arctan( \frac{3}{2} ) }{2} + \frac{\pi \: n}{2}$

$x = \frac{0.98279...}{2} + \frac{\pi \: n}{2}$

$x = 0.491395 + \frac{\pi \: n}{2}$