Advertisements
Advertisements
प्रश्न
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find tan (A + B)
Advertisements
उत्तर
Given, sin A = `(-5)/13`
We know that,
cos2A = 1 – sin2A = `1 - (-5/13)^2`
= `1 - 25/169`
= `144/169`
∴ cos A = `±12/13`
Since, `pi < "A" < (3pi)/2`
∴ ‘A’ lies in the 3rd quadrant
∴ cos A < 0
∴ cos A = `(-12)/13`
Also, cos B = `3/5`
∴ sin2B = 1 – cos2B = `1 - (3/5)^2`
= `1 - 9/25`
= `16/25`
∴ sin B = `±4/5`
Since, `(3pi)/2 < "B" < 2pi`
∴ ‘B’ lies in the 4th quadrant.
∴ sin B < 0
∴ sin B = `(-4)/5`
tan A = `sin"A"/cos"A" = ((-5/13))/((-12/13)) = 5/12`
tan B = `sin"B"/cos"B" = ((-4/5))/((3/5)) = -4/3`
tan (A + B) = `(tan"A" + tan"B")/(1 - tan"A" tan"B")`
= `(5/12 - 4/3)/(1 - (5/12)(-4/3)`
= `((-33/36))/((56/36))`
= `-33/56`
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:
`sqrt(2)cos (pi/4 - "A")` = cos A + sin 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 sin (A + B)
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find cos (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 .....
Select the correct option from the given alternatives :
The numerical value of tan 20° tan 80° cot 50° is equal to ______.
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)` = ?
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 = ____________.
If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.
`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` = ______
If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.
If tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to ______.
If α + β = `π/2` and β + γ = α, then the value of tan α is ______.
`(tan 80^circ - tan 10^circ)/(tan 70^circ)` is equal to ______.
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 ______.
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 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 ______.
