Advertisements
Advertisements
प्रश्न
Prove the following:
tan 20° tan 80° cot 50° = `sqrt(3)`
Advertisements
उत्तर
L.H.S. = tan 20° tan 80° cot 50°
= tan 20° tan 80° cot (90° − 40°)
= tan 20° tan 80° tan 40°
= tan 20° tan (60° + 20°) tan (60° − 20°)
`=tan20°((tan60°+tan20°)/(1-tan60°tan20°))((tan60°-tan20°)/(1+tan60°tan20°))`
= `tan20°((sqrt3+tan20°)/(1-sqrt3tan20°))((sqrt3-tan20°)/(1+sqrt3tan20°))`
= tan 20° `[((sqrt(3))^2-tan^2 20°)/(1^2-(sqrt3tan20°)^2)]`
= tan 20° `((3-tan^2 20°)/(1-3tan^2 20°))`
= `(3tan20°-tan^3 20°)/(1-3tan^2 20°)`
= tan 3 (20°)
= tan 60°
= `sqrt3`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the value of:
sin 15°
Find the values of:
tan 105°
Find the value of sin 690°.
Find the value of :
tan 225°
Find the value of :
tan (– 690°)
Find the value of :
cosec 780°
Find the value of :
cot (– 1110°)
Prove the following:
`cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]` = 1
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
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:
cosec 48° + cosec 96° + cosec 192° + cosec 384° = 0
Prove the following:
cos 36° = `(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 ____________.
If θ = `(17π)/3` then, tan θ – cot θ = ______.
The value of sin 495° is ______.
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 ______.
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^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 ______.
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 tan 315° cot(– 405°) + cot 495° tan (– 585°).
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 ______.
