Advertisements
Advertisements
Question
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
Options
`1/y - 1/x`
`1/x - 1/y`
`1/x + 1/y`
`(xy)/(x - y)`
Advertisements
Solution
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = `1/x + 1/y`
Explanation:
x = `sin"A"/cos"A" - sin"B"/cos"B"`
= `(sin"A"cos"B" - cos"A"sin"B")/(cos"A"cos"B")`
= `(sin("A" - "B"))/(cos"A" cos"B")`
y = `cos"B"/sin"B" - cos"A"/sin"A"`
= `(sin"A" cos"B" - cos"A"sin"B")/(sin"A"sin"B")`
= `(sin("A"- "B"))/(sin"A"sin"B")`
∴ `y/x = (cos"A"cos"B")/(sin"A"sin"B")` = cot A cot B
cot (A – B) = `(cot"A" cot"B" + 1)/(cot "B" - cot "A")`
= `(y/x + 1)/y`
= `(x + y)/(xy)`
= `1/x + 1/y`
APPEARS IN
RELATED QUESTIONS
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 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 `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:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
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
`(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 ______.
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
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)` = ____________.
In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.
`sqrt3 sin15^circ + cos15^circ` = ______
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` = ______
`(sin8A + sin2A)/(cos2A - cos8A)` 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 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 ______.
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
If tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), then ______.
If cos(A – B) = `3/5` and tan A tan B = 2, 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 ______.
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 ______.
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 ______.
The value of tan 3A – tan 2A – tan A is ______.
