Question

$6 sin x - 4 cos x=1/sin x$

Answer 1

$6sinx - 4cosx = frac{1}{sin x}|*sin x\ 6sin^2x - 4sinxcosx - 1 = 0\ 6sin^2x - 4sinxcosx - sin^2x - cos^2x = 0\ 5sin^2x - 4sinxcosx - cos^2x = 0 |*frac{1}{cos^x}\ 5tg^2x - 4tgx - 1 = 0\ t = tg x\ 5t^2 - 4t - 1=0\ D_1 = 4 + 5 = 9\ t_1 = -frac{1}{5}, t_2 = 1\ tg x = 1\ x = frac{pi}{4} + pi n\ tgx = -frac{1}{5}\ x = -arctg{1}{5} + pi k$