Question : $\cos \left(30^{\circ}+\theta\right)-\sin \left(60^{\circ}-\theta\right)=$ _____________.
Option 1: $\frac{\sqrt{3}}{2}$
Option 2: $0$
Option 3: $\frac{1}{2}$
Option 4: $\frac{1}{\sqrt{2}}$
Correct Answer: $0$
Solution :
$\cos (30^{\circ}+\theta)-\sin (60^{\circ}-\theta)$
= $\cos (30^{\circ}+\theta)-\cos(90^{\circ}-(60^{\circ}-\theta))$
= $\cos (30^{\circ}+\theta)-\cos(90^{\circ}-60^{\circ}+\theta)$
= $\cos (30^{\circ}+\theta)- \cos (30^{\circ}+\theta)$
= $0$
Hence, the correct answer is $0$.
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