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:
`sqrt(2)cos (pi/4 - "A")` = cos A + sin A
Prove the following:
`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`
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 :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
Select the correct option from the given alternatives :
The numerical value of tan 20° tan 80° cot 50° is equal to ______.
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x2 + y2 = ____________.
The value of sin 163° cos 347° + sin 167° sin 73° is ______
In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.
`(sec8A - 1)/(sec4A - 1)` = ______
If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
If sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
The value of cos 15° is ______.
The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` 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 tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to ______.
`(cos 9^circ + sin 9^circ)/(cos 9^circ - sin 9^circ)` is equal to ______.
If cos(81° + θ) = `sin(k/3 - θ)`, then k is equal to ______.
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 ______.
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 tan 3A – tan 2A – tan A is ______.
