Advertisements
Advertisements
प्रश्न
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
Advertisements
उत्तर
R.H.S. = tan(60° + A) tan(60° − A)
= `(sin(60^circ + "A")sin(60^circ - "A"))/(cos(60^circ + "A")cos(60^circ - "A")`
= `(2sin(60^circ + "A")sin(60^circ - "A"))/(2cos(60^circ + "A")cos(60^circ - "A")`
= `(cos[60^circ + "A" - (60^circ - "A")] - cos(60^circ + "A" + 60^circ - "A"))/(cos(60^circ + "A" + 60^circ - "A") + cos[60^circ + "A" - (60^circ - "A")]`
= `(cos2"A" - cos120^circ)/(cos120^circ - cos2"A")`
= `(cos2"A" - cos(180^circ - 60^circ))/(cos(180^circ - 60^circ) + cos2"A")`
= `(cos2"A" - (- cos 60^circ))/(- cos60^circ + cos2"A")`
= `(cos2"A" + 1/2)/(-1/2 + cos2"A")`
= `(2cos2"A" + 1)/(2cos2"A" - 1)`
= L.H.S.
APPEARS IN
संबंधित प्रश्न
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:
`(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 tan (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 :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
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 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 ______
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
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 ______.
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 α + β = `π/2` and β + γ = α, then the value of tan α is ______.
`(cos 9^circ + sin 9^circ)/(cos 9^circ - sin 9^circ)` 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 `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 ______.
sin 4θ can be written as ______.
If cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.
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 ______.
If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to ______.
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) = ______.
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 ______.
