Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Advertisements
उत्तर
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z
Now,
`tan θ = 1/(sqrt(3)) = tan π/6 ...[∵ tan π/6 = 1/(sqrt(3))]`
∴ the required general solution is
θ = nπ + `pi/(6)`, n ∈ Z.
APPEARS IN
संबंधित प्रश्न
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
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:
tan3θ = 3 tanθ.
State whether the following equation have solution or not?
3 tanθ = 5
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
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:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
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)` = _________.
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
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" = 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
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
The principal solutions of cot x = `sqrt3` are ______.
Which of the following equations has no solution?
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
The general solution of sin 2x = cos 2x is ______
The general solution of 4sin2 x = 1 is ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
Find the principal solutions of cot θ = 0
Which of the following equation has no solution?
The general solution of the equation tan2 x = 1 is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x 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.
If `2sin^-1 3/7` = cos–1β, then find the value of β.
