Question

sinx + cosx =square root 2

Answer 1

try squaring both sides and then you only need to apply a trig identity.

Answer 2

Square both sides:$$(\sin x+\cos x)^2=\sqrt2^2\\\sin^2x +2\sin x\cos x+\cos^2 x=2$$

Answer 3

then there are 2 trig identities you can use for the left side of the equation