Advertisements
Advertisements
प्रश्न
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (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`
sin (A + B) = sin A cos B + cos A sin B
= `(-5/13) (3/5) + (-12/13)(-4/5)`
= `-15/65 + 48/65`
= `33/65`
APPEARS IN
संबंधित प्रश्न
Prove the following:
`tan(pi/4 + theta) = (1 + tan theta)/(1 - tan theta)`
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)`
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:
3tan610° – 27 tan410° + 33tan210° = 1
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
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 = ____________.
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 ______
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
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 tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to ______.
`(cos 9^circ + sin 9^circ)/(cos 9^circ - sin 9^circ)` is equal to ______.
`(tan 80^circ - tan 10^circ)/(tan 70^circ)` is equal to ______.
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
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 ______.
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 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) = ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
The value of tan 3A – tan 2A – tan A is ______.
