Question

sin2x + 3cos2x = -1

Answer 1

is this an identity?

Answer 2

Solve: sin 2x + 3cos 2x = -1, Call tan a = 3 -> a = 71.56 deg.
sin 2x + (sin a/cos a)*cos 2x = -1
sin 2x*cos a + sin a*cos 2x = -cos x
Use the trig identity: sin (a + b) = sin a*cos b + sin b*cos a
sin (2x + a) = -cos a = -sin (90 - a)
sin (2x + 71,56) = -sin (90 - 71.56) = -sin 18.44 = sin (-18.44)
2x1 = -18.44 -> x1 = -9.22, and 2x2 = 180 + 18.44 = 198.44
--> x2 = 99.22

Answer 3

Check the answer. I am not sure about the computation.