Advertisements
Advertisements
Question
Select the correct option from the given alternatives :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
Options
sin A
cos A
– cos A
sin 2A
Advertisements
Solution
cos A
Explanation:
L.H.S. = sin [(n + 1)A] . sin [(n + 2)A] + cos [(n + 1)A] . cos [(n + 2)A]
= cos [(n + 2)A] . cos [(n + 1)A] + sin [(n + 2)A] . sin [(n + 1)A]
Let (n + 2)A = a and (n + 1)A = b …(i)
∴ L.H.S. = cos a . cos b + sin a . sin b
= cos (a − b)
= cos [(n + 2)A − (n + 1)A] ........[From (i)]
= cos [(n + 2 − n − 1)A]
= cos A
= R.H.S.
APPEARS IN
RELATED QUESTIONS
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
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find tan (A + B)
Prove the following:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x2 + y2 = ____________.
`sqrt3 sin15^circ + cos15^circ` = ______
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 = ______.
`(sec8A - 1)/(sec4A - 1)` = ______
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
If `0 < β < α < π/4, cos (α + β) = 3/5` and cos (α – β) = `4/5`, then sin 2α is equal to ______.
If `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β 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 ______.
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 ______.
`(tan 80^circ - tan 10^circ)/(tan 70^circ)` is equal to ______.
sin 4θ can be written as ______.
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 ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
