Question

sin (45 + θ) – cos (45 - θ) is

Answer 1

sin(A+B)-cos(A-B)

sinAcosB+cosAsinB-(cosAcosB+sinAsinB)
where A=45° and B is theta
just substitute its values

Answer 2

$\huge\doubleunderline{Solution}$

⠀⠀sin(45° + θ) - cos(45° - θ)

=> cos[90° - (45° + θ)] - cos(45° - θ)

⠀⠀⠀⠀⠀⠀⠀⠀⠀[since, cos(90° - θ) = sinθ]

=> cos(45° - θ) - cos(45° - θ) = 0