Question

prove that cos20.cos40.cos80=1/8

Answer 1

$\textbf{To prove:}$

$\cos\,20^{\circ}\,\cos\,40^{\circ}\,\cos\,80^{\circ}=\dfrac{1}{8}$

$\textbf{Solution:}$

$\text{Consider,}$

$\cos\,20^{\circ}\,\cos\,40^{\circ}\,\cos\,80^{\circ}$

$=\cos\,40^{\circ}\,\cos\,20^{\circ}\,\cos\,80^{\circ}$

$=\cos(60^{\circ}-20^{\circ})\,\cos\,20^{\circ}\,\cos(60^{\circ}+20^{\circ})$

$\text{Using the identity,}$

$\boxed{\bf\,\cos(60^{\circ}-A)\,\cos\,A\,\cos(60^{\circ}+A)=\dfrac{1}{4}\,cos3A}$

$=\dfrac{1}{4}\,cos\,3(20^{\circ})$

$=\dfrac{1}{4}\,cos\,60^{\circ}$

$=\dfrac{1}{4}(\dfrac{1}{2})$

$=\dfrac{1}{8}$

$\textbf{Answer:}$

$\boxed{\bf\,\cos\,20^{\circ}\,\cos\,40^{\circ}\,\cos\,80^{\circ}=\dfrac{1}{8}}$

Find more:

PROVE THAT:

cos 12 cos 24 cos 36 cos 48 Cos 60 cos 72 cos 84 equal = 1 / 128​

https://brainly.in/question/9849513

Answer 2

Answer:

the answer is 1/8

as cosA.cos60-A.cos60+A = 3A/4

cos3*20/4=1/8

hope this helps u ..