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:
`(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)`
Select the correct option from the given alternatives :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
Select the correct option from the given alternatives :
The numerical value of tan 20° tan 80° cot 50° 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:
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
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
The value of sin 163° cos 347° + sin 167° sin 73° is ______
`sqrt3 sin15^circ + cos15^circ` = ______
`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______
`(sec8A - 1)/(sec4A - 1)` = ______
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 = ______.
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
If sin A + cos A = `sqrt(2)`, then the value of cos2 A 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 A + B = 45°, then (cot A – 1) (cot B – 1) is equal to ______.
lf sin θ = cos θ, then the value of 2 tan2 θ + sin2 θ – 1 is equal to ______.
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin 31^circ) - 8 sin^2 30^circ` 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 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) = ______.
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 ______.
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) = ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
The value of tan 3A – tan 2A – tan A is ______.
