Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`
Advertisements
उत्तर
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z
Now,
tan `(2θ)/(3) = sqrt3`.
∴ tan `(2θ)/(3) = tan pi/(3) ...[∵ tan pi/(3) = sqrt(3)]`
∴ The required general solution is given by
`(2θ)/(3) = nπ + pi/(3)`, n ∈ Z
i.e. θ = `(3npi)/(2) + pi/(2)`, n ∈ Z
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
tan θ = – 1
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
cot 4θ = – 1
State whether the following equation has a solution or not?
2sinθ = 3
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
Select the correct option from the given alternatives:
The principal solutions of equation sin θ = `- 1/2` are ______.
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
Find the principal solutions of tan x = `-sqrt(3)`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
The general solution of sec θ = `sqrt2` is
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
Which of the following equations has no solution?
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The value of sin 18° is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general solution of 4sin2 x = 1 is ______.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
The number of principal solutions of tan 2θ = 1 is ______.
The general solution to cos100x – sin100x = 1 is ______.
If tan3θ = cotθ, then θ =
