Question

Proof: sin(x) + cos(x) = √2sin(x + π/4)

Answer 1

Hello : 
sin(x) + cos(x) = √2(1/√2 sin(x) +1/√2 cos(x))
but : 1/√2 = cos(π/4) =   sin( π/4)
sin(x) + cos(x) = √2( cos(π/4)sin(x) + sin( π/4) cos(x)) =√2sin(x + π/4)
because : cos(π/4)sin(x) + sin( π/4) cos(x)=sin(x + π/4) by identity :
sin(a+b) = sina cosb +cosa sinb