Advertisements
Advertisements
प्रश्न
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
विकल्प
`1/y - 1/x`
`1/x - 1/y`
`1/x + 1/y`
`(xy)/(x - y)`
Advertisements
उत्तर
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
संबंधित प्रश्न
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:
sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A
Prove the following:
`sqrt(2)cos (pi/4 - "A")` = cos A + sin A
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (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:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
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 = ____________.
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 = ______.
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 ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.
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 A + B = 45°, then (cot A – 1) (cot B – 1) 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 ______.
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
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) = ______.
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 ______.
The value of `sin π/16 sin (3π)/16 sin (5π)/16 sin (7π)/16` is ______.
If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
