Advertisements
Advertisements
प्रश्न
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
Advertisements
उत्तर
Since, tan30° = `1/sqrt(3)`
∴ tan3(10°) = `1/sqrt(3)`
∴ `(3tan10^circ - tan^3 10^circ)/(1 - 3tan^2 10^circ) = 1/sqrt(3)`
Squaring both the sides, we get
`((3tan10^circ - tan^3 10^circ)^2)/((1 - 3tan^2 10^circ)^2) = 1/3`
∴ `(9tan^2 10^circ - 6tan^4 10^circ + tan^6 10^circ)/(1 - 6tan^2 10^circ + 9tan^4 10^circ) = 1/3`
∴ 3(9tan210° – 6tan410°+ tan610°) = 1 – 6tan210° + 9tan410°
∴ 27tan210° – 18tan410° + 3tan610° = 1 – 6tan210° + 9tan410°
∴ 3tan610° – 27tan410° + 33tan210° = 1
APPEARS IN
संबंधित प्रश्न
Prove the following:
`tan(pi/4 + theta) = (1 + tan theta)/(1 - tan theta)`
Prove the following:
`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`
Prove the following:
`sqrt(2)cos (pi/4 - "A")` = cos A + sin A
Prove the following:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (A + B)
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find cos (A – B)
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) = _____
Select the correct option from the given alternatives :
The numerical value of tan 20° tan 80° cot 50° is equal to ______.
Prove the following:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.
In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.
`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______
`(sec8A - 1)/(sec4A - 1)` = ______
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
If sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
The value of cos 15° is ______.
If `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β is equal to ______.
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin 31^circ) - 8 sin^2 30^circ` is equal to ______.
If cos θ = `8/17` and θ lies in the 1st quadrant, then the value of cos(30° + θ) + cos(45° – θ) + cos(120° – θ) is ______.
If tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), then ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
sin 4θ can be written as ______.
If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
