Question

Find the value of:
Class 11
Maths​

Answer 1

Step-by-step explanation:

We have,

$\sec \bigg( \frac{\pi}{5} \bigg) . \cosec \bigg( \frac{\pi}{7} \bigg) . \cos \bigg( \frac{5\pi}{14} \bigg). \sin \bigg( \frac{3\pi}{10} \bigg)$

$= \cosec \bigg( \frac{\pi}{2} - \frac{\pi}{5} \bigg) . \sec \bigg( \frac{\pi}{2} - \frac{\pi}{7} \bigg) . \cos \bigg( \frac{5\pi}{14} \bigg). \sin \bigg( \frac{3\pi}{10} \bigg)$

$= \cosec \bigg( \frac{3\pi}{10} \bigg) . \sec \bigg( \frac{5\pi}{14} \bigg) . \cos \bigg( \frac{5\pi}{14} \bigg). \sin \bigg( \frac{3\pi}{10} \bigg)$

$= \cosec \bigg( \frac{3\pi}{10} \bigg) . \sin \bigg( \frac{3\pi}{10} \bigg). \sec \bigg( \frac{5\pi}{14} \bigg) . \cos \bigg( \frac{5\pi}{14} \bigg)$

$= 1 \times 1 = 1$