Advertisements
Advertisements
Question
If tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`
Advertisements
Solution
We have, tan A = `5/6` and tan B = `1/11`
∴ tan(A + B) = `(tan"A" + tan"B")/(1 - tan"A".tan"B")`
∴ tan(A + B) = `(5/6 + 1/11)/(1 - (5/6)(1/11))`
∴ tan(A + B) = `(55 + 6)/(66 - 5)`
∴ tan(A + B) = `61/61`
∴ tan(A + B) = 1
∴ tan(A + B) = 1 = `tan π/4`
∴ A + B = `π/4`
Hence proved.
APPEARS IN
RELATED QUESTIONS
Prove the following:
`tan(pi/4 + theta) = (1 + tan theta)/(1 - tan theta)`
Prove the following:
`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`
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 tan (A + B)
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:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
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) = ?
If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x2 + y2 = ____________.
In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
If A, B, C are the angles of ΔABC, then `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` = ______
If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.
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 ______.
`(tan 80^circ - tan 10^circ)/(tan 70^circ)` 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 ______.
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 ______.
cos2 76° + cos2 16° – cos 76° cos 16° is equal to ______.
The value of `sin π/16 sin (3π)/16 sin (5π)/16 sin (7π)/16` is ______.
The value of cot 70° + 4 cos 70° is ______.
If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
The value of tan 3A – tan 2A – tan A is ______.
