Advertisements
Advertisements
प्रश्न
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
Advertisements
उत्तर
L.H.S. = tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A
= `tan"A" + 2tan2"A" + 4tan4"A" + 8/(tan8"A")`
= `tan"A" + 2tan2"A" + 4tan4"A" + (8(1 - tan^2 4"A"))/(2tan4"A") ...[because tan2theta = (2tantheta)/(1 - tan^2theta)]`
= `tan"A" + 2tan2"A" + (8tan^2 4"A" + 8 - 8tan^2 4"A")/(2tan4"A")`
= `tan"A" + 2tan2"A" + 4/(tan4"A")`
= `tan"A" + 2tan2"A" + (4(1 - tan^2 2"A"))/(2tan2"A")`
= `tan"A" + (4tan^2 2"A" + 4 - 4tan^2 2"A")/(2tan2"A")`
= `tan"A" + 2/(tan2"A")`
= `tan"A" + (2(1 - tan^2"A"))/(2tan"A")`
= `(2tan^2"A" + 2 - 2tan^2"A")/(2tan"A")`
= `1/tan"A"`
= cot A
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following:
`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`
Prove the following:
sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A
Prove the following:
`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`
Prove the following:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (A + B)
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find cos (A – B)
If tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
Select the correct option from the given alternatives:
The value of `costheta/(1 + sin theta)` is equal to .....
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x2 + y2 = ____________.
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.
If sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
The value of cos 15° is ______.
If `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β is equal to ______.
If cos (α + β) = `4/5` and sin (α – β) = `5/13`, where `0 ≤ α, β ≤ π/4`, then tan 2α is equal to ______.
If α + β = `π/2` and β + γ = α, then the value of tan α is ______.
`(tan 80^circ - tan 10^circ)/(tan 70^circ)` is equal to ______.
If cos(81° + θ) = `sin(k/3 - θ)`, then k is equal to ______.
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin 31^circ) - 8 sin^2 30^circ` is equal to ______.
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
tan 100° + tan 125° + tan 100° tan 125° = ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
sin 4θ can be written as ______.
The value of cot 70° + 4 cos 70° is ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
