Question

guys plz answer this question...I will mark the best answer as brainliest​

Answer 1

Answer:

Step-by-step explanation:

Use the formula:

$2cosAcosB = cos(A+B) +cos(A-B)$

LHS:

$=\left( \cos \frac{\pi}{15} \cos \frac{4\pi}{15} \right) \left( \cos \frac{2\pi}{15} \cos \frac{7\pi}{15} \right)\\=(\frac{1}{2} (\cos \frac{\pi}{3} + \cos \frac{\pi}{5}) )(\frac{1}{2} (\cos \frac{3\pi}{5} +\cos \frac{\pi}{3} ) )\\=\frac{1}{4}(\frac{1}{2} +\cos \frac{\pi}{5})(\frac{1}{2} + \cos \frac{3\pi}{5})\\=\frac{1}{4}(\frac{1}{4} +\frac{1}{2}(\cos \frac{\pi}{5}+ \cos \frac{3\pi}{5}) + \cos \frac{\pi}{5} \cos \frac{3\pi}{5})$

$=\frac{1}{8} (\frac{1}{2} + \cos \frac{\pi}{5} + \cos \frac{3\pi}{5} + (\cos \frac{2\pi}{5}+\cos \frac{4\pi}{5}))$

Now cos(π-x)= -cos(x)

$=\frac{1}{8}(\frac{1}{2} +\cos \frac{\pi}{5} +\cos \frac{3\pi}{5}-\cos \frac{3\pi}{5}-\cos \frac{\pi}{5} )\\=\frac{1}{8}(\frac{1}{2})\\=\frac{1}{16}$