Advertisements
Advertisements
Question
Prove the following:
`cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]` = 1
Advertisements
Solution
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
RELATED QUESTIONS
Find the value of:
sin 15°
Find the values of:
tan 105°
Find the value of sin 690°.
Find the value of :
cos 315°
Find the value of :
tan (– 690°)
Find the value of :
cot (– 1110°)
Prove the following:
sec 840° . cot (– 945°) + sin 600° tan (– 690°) = `3/2`
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
Select the correct option from the given alternatives :
Let 0 < A, B < `pi/2` satisfying the equation 3 sin2A + 2 sin2B = 1 and 3 sin 2A − 2 sin 2B = 0 then A + 2B is equal to ______
Prove the following:
sin 20° sin 40° sin 80° = `sqrt(3)/8`
Prove the following:
cos 36° = `(sqrt(5) + 1)/4`
Prove the following:
`tan pi/8 = sqrt(2) - 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 `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8` 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)`.
If `cosA/3 = cosB/4 = 1/5, - π/2 < A < 0` and `- π/2 < B < 0`, then the value of 2 sin A + 4 sin B is ______.
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 ______.
If tan θ = `1/sqrt(7)`, then `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ))` is equal to ______.
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 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 ______.
cos 1°. cos 2°. cos 3° ...... cos 179° = ______.
