Question

sin (60° + θ) – cos (30° – θ) = ?
(a) 2sin θ
(b) 2cos θ
(c) 0
(d) 1

Answer 1

$$\begin{gathered} \sin \left(60°+\theta \right)-\cos \left(30°-\theta \right) \\ =\cos \left(90°-\left(60°+\theta \right)\right)-\cos \left(30°-\theta \right)\left(\because \sin \theta =\cos \left(90°-\theta \right)\right) \\ =\cos \left(90°-60°-\theta \right)-\cos \left(30°-\theta \right) \\ =\cos \left(30°-\theta \right)-\cos \left(30°-\theta \right) \\ =0 \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{c}\right). \end{gathered}$$