Question

Prove that Cos 10 Cos 30' Cos 50' Cos 70º = 3/16

Answer 1

Answer:

3/16

Step-by-step explanation:

Answer is

$\cos(10) \cos(30) \cos(50) \cos(70) \\ = \frac{ \sqrt{3} }{2} \times \cos(10) \cos(60 - 10) \cos(60 + 10) \\ = \frac{ \sqrt{3} }{2} \frac{1}{4} \cos(3 \times 10) \\ = \frac{ \sqrt{3} }{8} \times \cos(30) \\ = \frac{ \sqrt{3} }{8} \times \frac{ \sqrt{3} }{2} \\ = \frac{3}{16}$

We know that

$\cos( \alpha ) \cos(60 - \alpha ) \cos(60 + \alpha ) = \frac{1}{4} \cos(3 \alpha )$

Thank you