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:
`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)`
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 numerical value of tan 20° tan 80° cot 50° is equal to ______.
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)` = ?
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
`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 = ______.
`(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 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 ______.
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 ______.
`(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 ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
sin 4θ can be written as ______.
The value of `sin π/16 sin (3π)/16 sin (5π)/16 sin (7π)/16` 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 ______.
