Advertisements
Advertisements
Question
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Advertisements
Solution
cos 20° cos 40° cos 80°
= `((2 sin 20^circ)/(2 sin 20^circ))` cos 20° cos 40° cos 80°
[multiply and divide by 2 sin 20°]
`= ((2 sin 20^circ cos 20^circ) cos 40^circ cos 80^circ)/(2 sin 20^circ)`
`= (sin (2 xx 20^circ) cos 40^circ cos 80^circ)/(2 sin 20^circ)`
= `(sin 40^circ cos 40^circ cos 80^circ)/(2 sin 20^circ)`
(Multiply and divide by 2)
`= 1/2 xx ((2 sin 40^circ cos 40^circ))/(2 sin 20^circ) cos 80^circ`
`= 1/2 xx ((sin 2 xx 40^circ)cos 80^circ)/(2 sin 20^circ)`
`= 1/2 xx (sin 80^circ cos 80^circ)/(2 sin 20^circ)`
`= 1/2 xx 1/2 ((2 sin 80^circ cos 80^circ))/(2 sin 20^circ)`
`= 1/8 xx (sin 160^circ)/(sin 20^circ)`
`= 1/8 xx sin (180^circ - 20^circ)/(sin 20^circ)`
`= 1/8 xx sin 20^circ/sin 20^circ` ...[∵ sin(180° – θ) = sin θ]
`= 1/8 xx 1 = 1/8`
APPEARS IN
RELATED QUESTIONS
Prove that:
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
Prove that:
Prove that:
Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Express the following as the product of sine and cosine.
cos 2A + cos 4A
