Advertisements
Advertisements
प्रश्न
Prove the following:
`1/(tan3"A" - tan"A") - 1/(cot3"A" - cot"A")` = cot2A
Advertisements
उत्तर
L.H.S. = `1/(tan3"A" - tan"A") - 1/(cot3"A" - cot"A")`
= `1/(tan3"A" - tan"A") - 1/(1/(tan3"A") - 1/tan"A"`
= `1/(tan3"A" - tan"A") - (tan3"A"*tan"A")/(tan"A" - tan3"A")`
= `1/(tan3"A" - tan"A") + (tan3"A"*tan"A")/(tan3"A" - tan"A")`
= `(1 + tan3"A"*tan"A")/(tan3"A" - tan"A")`
= `1/(((tan3"A" - tan"A")/(1 + tan3"A"*tan"A"))`
= `1/(tan(3"A" - "A"))`
= `1/(tan2"A")`
= cot 2A
= R.H.S.
APPEARS IN
संबंधित प्रश्न
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:
16 sin θ cos θ cos 2θ cos 4θ cos 8θ = sin 16θ
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:
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 ......
Prove the following:
`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`
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 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 ______.
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 ______.
`(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 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` = ______.
(sec 2A + 1) sec2 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 ______.
