Advertisements
Advertisements
प्रश्न
Prove the following:
`cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]` = 1
Advertisements
उत्तर
L.H.S. = `cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]`
= sin x · cos x [tan x + cot x]
= `sinx * cosx[sinx/cosx + cosx/sinx]`
= `sinx*cosx[(sin^2x + cos^2x)/(sinx*cosx)]`
= `sinx*cosx xx 1/(sinx*cosx)`
= 1
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the values of:
cos 75°
Find the values of:
cot 225°
Find the value of sin 690°.
Find the value of :
sin (495°)
Find the value of :
tan 225°
Find the value of:
sec (–855°)
Find the value of :
cosec 780°
Prove the following:
`(cos(pi + x) cos(-x))/(sin(pi - x)cos(pi/2 + x))` = cot2x
Prove the following:
`("cosec"(90^circ - x)sin(180^circ - x)cot(360^circ - x))/(sec(180^circ + x)tan(90^circ + x)sin(-x))` = 1
Prove the following:
`(sin^3(pi + x)sec^2(pi - x)tan(2pi - x))/(cos^2(pi/2 + x)sin(pi - x)"cosec"^2 - x)` = tan3x
Select the correct option from the given alternatives :
If sin θ = n sin (θ + 2α), then tan (θ + α) is equal to
Prove the following:
tan 20° tan 80° cot 50° = `sqrt(3)`
Prove the following:
cosec 48° + cosec 96° + cosec 192° + cosec 384° = 0
Prove the following:
sin 20° sin 40° sin 80° = `sqrt(3)/8`
Prove the following:
tan6° tan42° tan66° tan78° = 1
If f(x) = `(2"x" + 3)/(3"x" - 2)`, `"x" ≠ 2/3`, then the function fof is ____________.
`(1 - 2[cos 60^circ - cos 80^circ])/(2 sin 10^circ)` = ______.
The value of sin(– 1125°) is ______.
The value of `sin((25π)/3)` is ______.
The value of `cos((41π)/4)` is ______.
The value of `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8` is ______.
Find the value of `cos ((29 π)/3)`.
The value of `(cot 54^circ)/(tan 36^circ) + (tan 20^circ)/(cot 70^circ)` is ______.
The value of `cos^2 π/16 + cos^2 (3π)/16 + cos^2 (5π)/16 + cos^2 (7π)/16` is ______.
If cos θ = `- sqrt(3)/2` and sin α = `-3/5`, where θ does not and α lies in the third quadrant, then `(2 tan α + sqrt(3) tan θ)/(cot^2 θ + cos alpha)` is equal to ______.
In a ΔABC, if ∠A = `π/2`, then cos2 B + cos2 C is equal to ______.
If sin A + sin B + sin C = 3, then cos A + cos B + cos C is equal to ______.
In a ΔPQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then ∠R is equal to ______.
The value of cos (270° + θ) cos (90° – θ) – sin (270° – θ) cos θ is ______.
The value of cos(– 870°) is ______.
The value of sin 135° cosec 225° tan 150° cot 315° is ______.
The value of `(cos(90^circ + θ) sec(-θ)tan(180^circ - θ))/(sec(360^circ - θ)sin(180^circ + θ)cot(90^circ - θ))` is ______.
The value of sin 150° cos 120° + cos 330° sin 660° is ______.
cos2 5° + cos2 10° + cos2 15° + .... + cos2 85° + cos2 90° is equal to ______.
sin (270° – θ) sin (90° – θ) – cos ( 270° – θ) cos (90° + θ) is ______.
