Advertisements
Advertisements
Question
Prove the following:
sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A
Advertisements
Solution
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:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
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 cos (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 :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
`sqrt3 sin15^circ + cos15^circ` = ______
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
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 `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is ______.
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 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 ______.
lf sin θ = cos θ, then the value of 2 tan2 θ + sin2 θ – 1 is equal to ______.
If cos(A – B) = `3/5` and tan A tan B = 2, then ______.
tan 100° + tan 125° + tan 100° tan 125° = ______.
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 ______.
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 ______.
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) = ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
The value of tan 3A – tan 2A – tan A is ______.
