Sin (3x + 10) = cos (x)

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