Advertisements
Advertisements
Question
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`
Advertisements
Solution
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
RELATED QUESTIONS
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
4sin2θ = 1.
Find the general solution of the following equation:
tan3θ = 3 tanθ.
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
cos2θ = – 1.
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
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 = _____
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the principal solutions of the following equation:
cot θ = 0
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
Find the general solutions of the following equation:
sin θ - cos θ = 1
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
State whether the following equation has a solution or not?
3 sin θ = 5
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
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 `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
Find the principal solutions of cosec x = 2
Find the principal solutions of sin x = `-1/2`
`cos^-1 (cos (4pi)/3)` = ______.
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
`int (sin (log x))^2/x` log x dx = ?
The principal solutions of cot x = `sqrt3` are ______.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
