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 (495°)
Find the value of :
cos (600°)
Find the value of :
sec 240°
Find the value of:
sec (–855°)
Prove the following:
`(cos(pi + x) cos(-x))/(sin(pi - x)cos(pi/2 + x))` = cot2x
Prove the following:
sec 840° . cot (– 945°) + sin 600° tan (– 690°) = `3/2`
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
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:
sin 36° = `(sqrt(10 - 2sqrt(5)))/4`
Prove the following:
sin47° + sin61° − sin11° − sin25° = cos7°
If θ = `(17π)/3` then, tan θ – cot θ = ______.
The value of sin 495° is ______.
The value of `sin((25π)/3)` is ______.
The value of `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8` 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 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 ______.
cos 1° + cos 2° + cos 3° + ... + cos 180° is equal to ______.
If sin A + sin B + sin C = 3, then cos A + cos B + cos C is equal to ______.
The value of cos (270° + θ) cos (90° – θ) – sin (270° – θ) cos θ is ______.
The value of the expression sin6 θ + cos6 θ + 3 sin2 θ . cos2 θ is ______.
The value of cos(– 870°) is ______.
The value of sin 135° cosec 225° tan 150° cot 315° is ______.
cos2 5° + cos2 10° + cos2 15° + .... + cos2 85° + cos2 90° is equal to ______.
cos 1°. cos 2°. cos 3° ...... cos 179° = ______.
If x ≠ 0, then `(sin(pi + x)cos(pi/2 + x)tan((3pi)/2 - x)cot(2pi - x))/(sin(2pi - x)cos(2pi + x)cosec(-x)sin((3pi)/2 + x))` =
