Advertisements
Advertisements
प्रश्न
Select the correct option from the given alternatives :
The numerical value of tan 20° tan 80° cot 50° is equal to ______.
विकल्प
`sqrt(3)`
`1/sqrt(3)`
`2sqrt(3)`
`1/(2sqrt(3)`
Advertisements
उत्तर
`sqrt(3)`
Explanation;
L.H.S. = tan 20° tan 80° cot 50°
= tan 20° tan 80° cot (90° − 40°)
= tan 20° tan 80° tan 40°
= tan20° 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
Prove the following:
sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A
Prove the following:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
Select the correct option from the given alternatives :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?
The value of sin 163° cos 347° + sin 167° sin 73° is ______
In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.
`(sec8A - 1)/(sec4A - 1)` = ______
If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.
If `0 < β < α < π/4, cos (α + β) = 3/5` and cos (α – β) = `4/5`, then sin 2α is equal to ______.
If `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β is equal to ______.
If α + β = `π/2` and β + γ = α, then the value of tan α is ______.
`(tan 80^circ - tan 10^circ)/(tan 70^circ)` is equal to ______.
If cos(81° + θ) = `sin(k/3 - θ)`, then k is equal to ______.
lf sin θ = cos θ, then the value of 2 tan2 θ + sin2 θ – 1 is equal to ______.
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin 31^circ) - 8 sin^2 30^circ` is equal to ______.
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
If cos(A – B) = `3/5` and tan A tan B = 2, then ______.
cos2 76° + cos2 16° – cos 76° cos 16° is equal to ______.
The value of cot 70° + 4 cos 70° is ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
