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Question:

The value of sin 73° + cos 137° is:

Explanation:

We know, sin A - sin B = 2 × $\cos \left(\frac{\mathrm{A}+\mathrm{B}}{2}\right)$ × $\sin \left(\frac{\mathrm{A}-\mathrm{B}}{2}\right)$

Given, sin 73° + cos 137° = sin 73° + cos (90 + 47)° = sin 73° - sin 47°

⇒ sin 73° - sin 47° = 2 × $\cos \left(\frac{73+47}{2}\right)$ × $\sin \left(\frac{73-47}{2}\right)$

⇒ sin 73° - sin 47° = 2 × cos 60° × sin 13°

⇒ sin 73° - sin 47° = 2 × 1/2 × sin 13°

⇒ sin 73° - sin 47° = sin 13°

Hence, option (b).