In general cos x = cos a has solutions x = ±a + 360°k, integer k
sin(3x + 10) = cos x
Assuming that's 10°
cos(90 - (3x+10)) = cos x
cos(80 - 3x) = cos x
80 - 3x = ±x + 360°k
Plus first,
80-3x = x + 360°k
-4x = -80 + 360°k
x =20° - 90°k
Minus next,
80 - 3x = -x + 360°k
-2x = -80 + 360°k
x = 40° - 180°k
k runs over all the integers so we can flip the sign.
Answer: x = 20° + 90°k or x = 40° + 180°k, integer k
