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:
`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 tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`
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:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
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 = ______.
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
If A, B, C are the angles of ΔABC, then `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` = ______
`(sin8A + sin2A)/(cos2A - cos8A)` 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 = ______.
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 ______.
If A + B = 45°, then (cot A – 1) (cot B – 1) is equal to ______.
If tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to ______.
If α + β = `π/2` and β + γ = α, then the value of tan α is ______.
`(cos 9^circ + sin 9^circ)/(cos 9^circ - sin 9^circ)` is equal to ______.
`(tan 80^circ - tan 10^circ)/(tan 70^circ)` is equal to ______.
If tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), then ______.
sin 4θ can be written as ______.
The value of `sin π/16 sin (3π)/16 sin (5π)/16 sin (7π)/16` is ______.
If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
