Advertisements
Advertisements
प्रश्न
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find cos (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`
cos(A – B) = cosA cosB +sinA sinB
= `(-12/13)(3/5)+(-5/13)(-4/5)`
= `-36/65+20/65`
= `-16/65`
APPEARS IN
संबंधित प्रश्न
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)`
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
`(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 ______.
cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?
The value of sin 163° cos 347° + sin 167° sin 73° is ______
`sqrt3 sin15^circ + cos15^circ` = ______
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
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 sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
The value of cos 15° is ______.
If `0 < β < α < π/4, cos (α + β) = 3/5` and cos (α – β) = `4/5`, then sin 2α is equal to ______.
If tan α = k cot β, then `(cos(α - β))/(cos(α + β))` 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 tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), 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) = ______.
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 ______.
The value of cot 70° + 4 cos 70° is ______.
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 ______.
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 ______.
