Advertisements
Advertisements
प्रश्न
Prove the following:
`(sin5x - 2sin3x + sinx)/(cos5x - cosx)` = tanx
Advertisements
उत्तर
L.H.S. = `(sin5x - 2sin3x + sinx)/(cos5x - cosx)`
= `((sin5x + sinx) - 2sin3x)/(cos5x - cosx)`
= `(2sin((5x + x)/2)*cos((5x - x)/2)-2sin3x)/(-2sin((5x + x)/2)*sin((5x - x)/2)`
= `(2sin3x*cos2x - 2sin3x)/(-2sin3x*sin2x)`
= `(2sin3x(cos2x - 1))/(-2sin3x*sin2x)`
= `(1 - cos2x)/(sin2x)`
= `(2sin^2x)/(2sinx cosx)`
= `sinx/cosx`
= tanx
= 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 = `4sin^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:
`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:
`(sin^2(-160^circ))/(sin^(2)70^circ) + sin(180^circ - theta)/sintheta` = sec220°
Prove the following:
`(2cos 4x + 1)/(2cosx + 1)` = (2 cos x – 1) (2 cos 2x – 1)
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 ______.
Prove the following:
cos22x − cos26x = sin4x sin8x
Prove the following:
cot4x (sin5x + sin3x) = cotx (sin5x − sin3x)
cos4 θ – sin4 θ is equal to ______.
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 ______.
If `x + 1/x` = 2 cos θ, then `x^n + 1/x^n` is equal to ______.
`(1 - tan^2(45^circ - A))/(1 + tan^2(45^circ - A))` is equal to ______.
If `sqrt((1 + cos A)/(1 - cos A)) = x/y`, then the value of tan A is ______.
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 ______.
`(sin(90^circ - θ) sin θ)/tanθ + sin^2 θ` is equal to ______.
If θ is acute and `(cos^2θ)/(cot^2 θ - cos^2 θ)` = 3, then 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 `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 ______.
If `(2 sin α)/({1 + cos α + sin α})` = y, then `({1 - cos α + sin α})/(1 + sin α)` = ______.
If tan α = `1/7`, tan β = `1/3`, then cos 2α = ______.
2 sin A cos3 A – 2 sin3 A cos A = ______.
The expression `2 cos π/13. cos (9π)/13 + cos (3π)/13 + cos (5π)/13` is equal to ______.
