Advertisements
Advertisements
Question
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Options
nπ
`("n"pi)/6`
`"n"pi +- pi/4`
`("n"pi)/2`
Solution
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is `("n"pi)/6`.
Explanation:
tan (A + B + C) = `(tan A + tan B - tanA. tan B. tan C)/(1 - tan A.tan B - tan B.tanC - tan C.tan A)`
Since, tan θ + tan 2θ + tan 3θ = tan θ.tan
2θ.tan 3θ,
we get, tan (θ + 2θ + 3θ) = θ
∴ tan 6θ = 0
∴ 6θ = nπ
θ = `(npi)/6`
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
cot θ = 0
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`.
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
sin θ = tan θ.
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
2sinθ = 3
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:
If cos pθ = cos qθ, p ≠ q, then ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
Select the correct option from the given alternatives:
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______
`"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:
sin θ - cos θ = 1
If 2 tan-1(cos x) = tan-1(2 cosec x), 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 = 1/3 tan^-1 11/2`
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of cosec x = 2
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
The principal solutions of cot x = `sqrt3` are ______.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of cot θ + tan θ = 2 is ______.
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
Which of the following equation has no solution?
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
