Question:
sin (60° + θ) – cos (30° – θ) = ?
(a) 2sin θ
(b) 2cos θ
(c) 0
(d) 1
Solution:
$\sin \left(60^{\circ}+\theta\right)-\cos \left(30^{\circ}-\theta\right)$
$=\cos \left(90^{\circ}-\left(60^{\circ}+\theta\right)\right)-\cos \left(30^{\circ}-\theta\right) \quad\left(\because \sin \theta=\cos \left(90^{\circ}-\theta\right)\right)$
$=\cos \left(90^{\circ}-60^{\circ}-\theta\right)-\cos \left(30^{\circ}-\theta\right)$
$=\cos \left(30^{\circ}-\theta\right)-\cos \left(30^{\circ}-\theta\right)$
$=0$
Hence, the correct option is (c).