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)`
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 tan (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) = _____
Prove the following:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
The value of `tan^-1 (1/3) + tan^-1 (1/5) + tan^-1 (1/7) + tan^-1 (1/8)`is ______.
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 = ____________.
If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.
`sqrt3 sin15^circ + cos15^circ` = ______
`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______
`(sec8A - 1)/(sec4A - 1)` = ______
If sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
If `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β is equal to ______.
If A + B = 45°, then (cot A – 1) (cot B – 1) is equal to ______.
If α + β = `π/2` and β + γ = α, then the value of tan α is ______.
`(cos 9^circ + sin 9^circ)/(cos 9^circ - sin 9^circ)` is equal to ______.
`(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 ______.
lf sin θ = cos θ, then the value of 2 tan2 θ + sin2 θ – 1 is equal to ______.
If cos θ = `8/17` and θ lies in the 1st quadrant, then the value of cos(30° + θ) + cos(45° – θ) + cos(120° – θ) is ______.
If tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), then ______.
tan 100° + tan 125° + tan 100° tan 125° = ______.
If `π/2 < α < π, π < β < (3π)/2`; sin α = `15/17` and tan β = `12/5`, then the value of sin(β – α) is ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
sin 4θ can be written as ______.
If cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.
The value of cot 70° + 4 cos 70° is ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
