Advertisements
Advertisements
प्रश्न
Prove the following:
sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove the following:
`sqrt(2)cos (pi/4 - "A")` = cos A + sin 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)`
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)
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:
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)` = ?
The value of `tan^-1 (1/3) + tan^-1 (1/5) + tan^-1 (1/7) + tan^-1 (1/8)`is ______.
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______
If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.
If sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
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 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 ______.
`(cos 9^circ + sin 9^circ)/(cos 9^circ - sin 9^circ)` 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 ______.
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 cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.
cos2 76° + cos2 16° – cos 76° cos 16° is equal to ______.
If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
