Advertisements
Advertisements
प्रश्न
Prove the following:
cot4x (sin5x + sin3x) = cotx (sin5x − sin3x)
Advertisements
उत्तर
We have to prove that,
cot4x (sin5x + sin3x) = cot x (sin5x – sin3x)
i.e., to prove that,
`(sin5x + sin3x)/(sin5x - sin3x) = cotx/(cot4x)`
L.H.S. = `(sin5x + sin3x)/(sin5x - sin3x)`
= `(2sin((5x + 3x)/2)*cos((5x - 3x)/2))/(2cos((5x + 3x)/2)*sin((5x - 3x)/2)`
= `(2sin4x*cosx)/(2cos4x*sinx)`
= tan4x · cotx
= `cotx/(cot4x)`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following:
`(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)` = tan72°
Prove the following:
(sin 3x + sin x)sin x + (cos 3x – cos x) cos x = 0
Prove the following:
(cos x + cos y)2 + (sin x – sin y)2 = `4cos^2 ((x + y))/2`
Prove the following:
tan x + cot x = 2 cosec 2x
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:
`1/(tan3"A" - tan"A") - 1/(cot3"A" - cot"A")` = cot2A
Prove the following:
cos7° cos14° cos28° cos56° = `sin68^circ/(16cos83^circ)`
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 :
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:
sin26x − sin24x = sin2x sin10x
Prove the following:
cos22x − cos26x = sin4x sin8x
Prove the following:
`sqrt(3) "cosec"20^circ - sec20^circ` = 4
`sqrt(3) "cosec" 20^circ - sec 20^circ` is equal to ______.
If `x + 1/x` = 2 cos θ, then `x^n + 1/x^n` is equal to ______.
If sin 4A – cos 2A = cos 4A – sin 2A `("where", 0 < A < π/4)`, then the value of tan 4A is ______.
The value of `(cos^3θ - cos 3θ)/cosθ + (sin^3θ + sin 3θ)/sinθ` is ______.
If tan x = sin 45° cos 45° + sin 30°, then x is equal to ______.
The value of `(1 + cos π/6)(1 + cos π/3)(1 + cos (2π)/3)(1 + cos (7π)/6)` is equal to ______.
If `tan x + tan(π/3 - x) tan ((2π)/3 + x)` = 3, then ______.
If sin θ = `12/13, (0 < θ < π/2)` and cos `phi = - 3/5, (π < phi < (3π)/2)`. Then, sin(θ + `phi`) will be ______.
`(sin θ + sin 2θ)/(1 + cos θ + cos 2θ)` = ______.
`(sin 3θ - cos 3θ)/(sin θ + cos θ) + 1` = ______.
If tan β = cos θ tan α, then `tan^2 θ/2` = ______.
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 ______.
The expression `2 cos π/13. cos (9π)/13 + cos (3π)/13 + cos (5π)/13` is equal to ______.
