Advertisements
Advertisements
Question
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
Advertisements
Solution
L.H.S. = `(sin^3(pi + x)sec^2(pi - x)tan(2pi - x))/(cos^2(pi/2 + x)sin(pi - x)"cosec"^2 (- x))`
= `([sin(pi + x)]^3 [sec(pi - x)]^2 tan(2pi - x))/([cos(pi/2 + x)]^2 sin(pi - x)*(-"cosec")^2`
= `((-sinx)^3(-secx)^2(-tanx))/((-sinx)^2*sinx*"cosec"^2x)`
= `((-sin^3x)*sec^2x*(-tanx))/(sin^2x*sinx*1/sin^2x)`
= `(sin^3x*sec^2x*tanx)/sinx`
= `sin^2x*1/cos^2x tanx`
= tan2x.tanx
= tan3x
= R.H.S.
APPEARS IN
RELATED QUESTIONS
Find the values of:
cos 75°
Find the values of:
tan 105°
Find the value of :
sin (495°)
Find the value of :
tan (– 690°)
Find the value of :
sec 240°
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:
cosθ + sin (270° + θ) − sin (270° − θ) + cos (180° + θ) = 0
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:
sin 18° = `(sqrt(5) - 1)/4`
Prove the following:
`tan pi/8 = sqrt(2) - 1`
Prove the following:
tan6° tan42° tan66° tan78° = 1
Prove the following:
sin47° + sin61° − sin11° − sin25° = cos7°
If a = sin 175°+ cos 175°, then ______.
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 `cos((41π)/4)` is ______.
The value of `2 cot^2(π/6) + 4 tan^2(π/6) - 3 "cosec"(π/6)` 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 480° sin 150° + sin 600° cos 390° is ______.
The value of `cos^2 π/16 + cos^2 (3π)/16 + cos^2 (5π)/16 + cos^2 (7π)/16` is ______.
cos 1° + cos 2° + cos 3° + ... + cos 180° is equal to ______.
If `sin A - sqrt(6) cos A = sqrt(7) cos A`, then `cos A + sqrt(6) sin A` is equal to ______.
The value of the expression sin6 θ + cos6 θ + 3 sin2 θ . cos2 θ is ______.
The value of cos(– 870°) 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 ______.
sin (270° – θ) sin (90° – θ) – cos ( 270° – θ) cos (90° + θ) is ______.
