Advertisements
Advertisements
प्रश्न
Prove the following:
`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`
उत्तर
L.H.S. = `(cos(x - y))/(cos(x + y))`
= `(cosx cosy + sinx siny)/(cos x cos y - sin x sin y)`
Dividing numerator and denominator by sin x sin y, we get
L.H.S. = `(((cosx cosy)/(sinx sin y) + 1))/(((cosx cos y)/(sinx sin y) - 1)`
= `(cotx coty + 1)/(cotx coty - 1)`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
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:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
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 (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)` = ____________.
The value of sin 163° cos 347° + sin 167° sin 73° is ______
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
The value of cos 15° is ______.
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 cos (α + β) = `4/5` and sin (α – β) = `5/13`, where `0 ≤ α, β ≤ π/4`, then tan 2α is equal to ______.
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 ______.
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 ______.
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
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 ______.
The value of `sin π/16 sin (3π)/16 sin (5π)/16 sin (7π)/16` 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) = ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
The value of tan 3A – tan 2A – tan A is ______.
