Advertisements
Advertisements
प्रश्न
Prove the following:
`(2cos 4x + 1)/(2cosx + 1)` = (2 cos x – 1) (2 cos 2x – 1)
Advertisements
उत्तर
L.H.S. = `(2cos 4x + 1)/(2cosx + 1)`
= `(2[2cos^2(2x) - 1] + 1)/(2cos x + 1)` ...[∵ cos 2θ = 2 cos2 θ – 1]
= `(4cos^2 2x - 2 + 1)/(2cos x + 1)`
= `((2cos 2x)^2 - (1)^2)/(2cos x + 1)`
= `((2cos 2x + 1)(2cos 2x - 1))/(2cos x + 1)`
= `([2(2cos^2 x - 1) + 1](2cos 2x - 1))/(2cosx + 1)`
= `((4cos^2 x - 2 + 1)(2cos 2x - 1))/(2cos x + 1)`
= `([(2cos x)^2 - (1)^2](2cos 2x - 1))/(2cos x + 1)`
= `((2cos x + 1)(2cos x - 1)(2cos 2x - 1))/(2cos x + 1)`
= (2 cos x – 1) (2 cos 2x – 1)
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following:
`(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)` = tan72°
Prove the following:
`(cot"A"cot4"A" + 1)/(cot"A" cot4"A" - 1) = (cos3"A")/(cos5"A")`
Prove the following:
(cos x + cos y)2 + (sin x – sin y)2 = `4cos^2 ((x + y))/2`
Prove the following:
16 sin θ cos θ cos 2θ cos 4θ cos 8θ = sin 16θ
Prove the following:
`cosx/(1 + sinx) = (cot(x/2) - 1)/(cot(x/2) + 1)`
Prove the following:
`(tan(theta/2) + cot(theta/2))/(cot(theta/2) - tan(theta/2))` = secθ
Prove the following:
cos7° cos14° cos28° cos56° = `sin68^circ/(16cos83^circ)`
Prove the following:
`(sin^2(-160^circ))/(sin^(2)70^circ) + sin(180^circ - theta)/sintheta` = sec220°
Prove the following:
cos2x + cos2(x + 120°) + cos2(x – 120°) = `3/2`
Prove the following:
2cosec 2x + cosec x = `secx cot(x/2)`
Prove the following:
`4 cos x. cos(x + pi/3) . cos (x - pi/3)` = cos 3x
Select the correct option from the given alternatives :
The value of cos A cos (60° – A) cos (60° + A) is equal to ......
Select the correct option from the given alternatives:
The value of `sin pi/14sin (3pi)/14sin (5pi)/14sin (7pi)/14sin (9pi)/14sin (11pi)/14sin (13pi)/14` is ______.
Select the correct option from the given alternatives :
If α + β + γ = π then the value of sin2α + sin2β – sin2γ is equal to …......
Prove the following:
`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`
Prove the following:
`(sin5x - 2sin3x + sinx)/(cos5x - cosx)` = tanx
Prove the following:
cos22x − cos26x = sin4x sin8x
Prove the following:
`sqrt(3) "cosec"20^circ - sec20^circ` = 4
`(1 - tan^2(45^circ - A))/(1 + tan^2(45^circ - A))` is equal to ______.
If tan A and tan B are the roots of x2 – ax + b = 0, then the value of sin2(A + B) is ______.
cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x is equal to ______.
If θ is acute and `(cos^2θ)/(cot^2 θ - cos^2 θ)` = 3, then θ is equal to ______.
If `(2 sin α)/({1 + cos α + sin α})` = y, then `({1 - cos α + sin α})/(1 + sin α)` = ______.
`(sin θ + sin 2θ)/(1 + cos θ + cos 2θ)` = ______.
`(sin 3θ - cos 3θ)/(sin θ + cos θ) + 1` = ______.
(sec 2A + 1) sec2 A = ______.
2 sin A cos3 A – 2 sin3 A cos A = ______.
The value of `sin π/10` is ______.
The value of sin 3A sin3 A + cos 3A cos3 A is ______.
