Advertisements
Advertisements
Question
Prove the following:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Advertisements
Solution
sin 2A = λsin 2B
∴ `(sin 2"A")/(sin 2"B") = lambda/1`
∴ `(sin2"A" + sin2"B")/(sin2"A" - sin2"B") = (lambda + 1)/(lambda - 1)`
∴ `(2sin((2"A" + 2"B")/2)*cos((2"A" - 2"B")/2))/(2cos ((2"A" + 2"B")/2)*sin((2"A" - 2"B")/2)) = (lambda + 1)/(lambda - 1)`
∴ `(sin("A" + "B")*cos("A" - "B"))/(cos("A" + "B")*sin("A" - "B")) = (lambda + 1)/(lambda - 1)`
∴ tan(A + B) · cot(A – B) = `(lambda + 1)/(lambda - 1)`
∴ `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`.
APPEARS IN
RELATED QUESTIONS
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)`
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 numerical value of tan 20° tan 80° cot 50° is equal to ______.
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
`(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 ______.
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.
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 = ______.
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
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` = ______
`(sec8A - 1)/(sec4A - 1)` = ______
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
The value of cos 15° is ______.
If `0 < β < α < π/4, cos (α + β) = 3/5` and cos (α – β) = `4/5`, then sin 2α 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 ______.
If cos(A – B) = `3/5` and tan A tan B = 2, then ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
If cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.
cos2 76° + cos2 16° – cos 76° cos 16° is equal to ______.
If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to ______.
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 ______.
