Question

cosx+sinx=$sqrt 2$

Answer 1

cosx+sinx=√2
(cosx+sinx)²=(√2)²
cos²x+2cosxsinx+sin²x=2
1+2sinxcosx=2
2sinxcosx=1
sin2x=1
2x=π/2+2πn
x=π/4+2πn,    n ∈ Ζ