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:
tan10° + tan35° + tan10°.tan35° = 1
Prove the following:
`(cot"A"cot4"A" + 1)/(cot"A" cot4"A" - 1) = (cos3"A")/(cos5"A")`
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:
`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:
`4 cos x. cos(x + pi/3) . cos (x - pi/3)` = cos 3x
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:
sin26x − sin24x = sin2x sin10x
Prove the following:
`sqrt(3) "cosec"20^circ - sec20^circ` = 4
Let α and β be such that π < α – β < 3π. If sin α + sin β = `- 21/65` and cos α + cos β = `-27/65`, then the value of `cos ((α - β))/2` is ______.
`(1 - tan^2(45^circ - A))/(1 + tan^2(45^circ - A))` is equal to ______.
If cos 2α = `(3 cos 2β - 1)/(3 - cos 2β)`, then tan α 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 ______.
If sin 4A – cos 2A = cos 4A – sin 2A `("where", 0 < A < π/4)`, then the value of tan 4A is ______.
For any angle θ, the expression `(2 cos 8θ + 1)/(2 cos θ + 1)` is equal to ______.
cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x is equal to ______.
If tan x = sin 45° cos 45° + sin 30°, then x is equal to ______.
If sin θ = `1/2` and θ is acute, then (3 cos θ – 4 cos3 θ) 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 sin θ = `12/13, (0 < θ < π/2)` and cos `phi = - 3/5, (π < phi < (3π)/2)`. Then, sin(θ + `phi`) will be ______.
If tan α = `1/7`, tan β = `1/3`, then cos 2α = ______.
2 sin A cos3 A – 2 sin3 A cos A = ______.
The value of `sin π/10` is ______.
The value of cos 6x is equal to ______.
The value of sin 3A sin3 A + cos 3A cos3 A is ______.
