Q240 / 270 · NDA 2016 (Phase 1) · Mathematics
If $A=\left(\cos 12^{\circ}-\cos 36^{\circ}\right)\left(\sin 96^{\circ}+\sin 24^{\circ}\right)$ and $\mathrm{B}=\left(\sin 60^{\circ}-\sin 12^{\circ}\right)\left(\cos 48^{\circ}-\cos 72^{\circ}\right)$, then what is $\frac{\mathrm{A}}{\mathrm{B}}$ equal to?
- A–1
- B0
- Correct answerC1
- D2
Solution
$\begin{aligned} & \text { Given } A=\left(\cos 12^{\circ}-\cos 36^{\circ}\right)\left(\sin 96^{\circ}+\sin 24^{\circ}\right) \\ & B=\left(\sin 60^{\circ}-\sin 12^{\circ}\right)\left(\cos 48^{\circ}-\cos 72^{\circ}\right) \\ & \frac{A}{B}=\frac{\left[2 \sin 24^{\circ} \sin 12^{\circ}\right]\left[2 \sin 60^{\circ} \cos 36^{\circ}\right]}{\left[2 \cos 36^{\circ} \sin 24^{\circ}\right]\left[2 \sin 60^{\circ} \sin 12^{\circ}\right]} \\ & \Rightarrow \frac{A}{B}=1\end{aligned}$
Hence, the correct answer is option: 'C'.