Question

Prove that Sin(pi/4 + x) + sin (pi/4 - x) = root 2 cos x ?

Answer 1

`LHS=sin(45°+x)+sin(45°-x)`

`=2sin((45+x+45-x)/2)*cos((45+x-45+x)/2)`

`=2*sin45*cosx`

`=(sqrt2*cancelsqrt2)*(1/cancelsqrt2)cosx=sqrt2cosx=RHS`