Question

sin (45° + θ) – cos (45° – θ) = ?
(a) 0
(b) 1
(c) 2
(d) –2

Answer 1

$$\begin{gathered} \sin \left(45°+\theta \right)-\cos \left(45°-\theta \right) \\ =\cos \left(90°-\left(45°+\theta \right)\right)-\cos \left(45°-\theta \right)\left(\because \sin \theta =\cos \left(90°-\theta \right)\right) \\ =\cos \left(90°-45°-\theta \right)-\cos \left(45°-\theta \right) \\ =\cos \left(45°-\theta \right)-\cos \left(45°-\theta \right) \\ =0 \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{a}\right). \end{gathered}$$