Advertisements
Advertisements
प्रश्न
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
Advertisements
उत्तर
LHS = cos 20° cos 40° cos 60° cos 80°
`= cos 20° cos 40° (1/2) cos 80° [∵ cos 60° = 1/2]`
`= 1/2 (cos 20° cos 40° cos 80°)`
`= 1/2 ((2 sin 20^circ)/(2 sin 20^circ))` (cos 20° cos 40° cos 80°)
[multiply and divide by 2 sin 20°]
`= 1/2 (((2 sin 20^circ cos 20^circ)cos 40^circ cos 80^circ)/(2 sin 20^circ))`
`= 1/2 (sin (2 xx 20^circ) cos 40^circ cos 80^circ)/(2 sin 20^circ)`
`= 1/2 (sin 40^circ cos 40^circ cos 80^circ)/(2 sin 20^circ)`
`= 1/2 1/2 xx (2 sin 40^circ cos 40^circ)/(2 sin 20^circ) xx cos 80^circ`
[multiply and divide by 2]
`= 1/2 1/2 xx ((sin 2 xx 40^circ)cos 80^circ)/(2 sin 20^circ)`
`= 1/2 1/2 xx (sin 80^circ cos 80^circ)/(2 sin 20^circ)`
`= 1/2 1/2 xx 1/2 ((2 sin 80^circ cos 80^circ))/(2 sin 20^circ)`
`= 1/2 1/8 xx (sin 160^circ)/(sin 20^circ)`
`= 1/8 xx (sin (180^circ - 20^circ))/(sin 20^circ)`
`= 1/2 1/8 xx (sin 20^circ)/(sin 20^circ)`
`= 1/2 1/8 xx 1`
`= 1/2 (1/8) = 1/16`
Hence Proved.
APPEARS IN
संबंधित प्रश्न
Prove that:
Prove that tan 20° tan 30° tan 40° tan 80° = 1.
Express each of the following as the product of sines and cosines:
sin 2x + cos 4x
Prove that:
Prove that:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
Prove that:
If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ.
If (cos α + cos β)2 + (sin α + sin β)2 = \[\lambda \cos^2 \left( \frac{\alpha - \beta}{2} \right)\], write the value of λ.
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
