Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
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:
tan θ = - 1
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`.
Find the general solution of the following equation:
4cos2θ = 3.
Find the general solution of the following equation:
sin θ = tan θ.
Find the general solution of the following equation:
cosθ + sinθ = 1.
State whether the following equation have solution or not?
3 tanθ = 5
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
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 = ______
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:
In any ΔABC, if acos B = bcos A, then the triangle is
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:
`tan^2 theta = 3`
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 Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
If x, y, z are positive, then prove that
`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`
Find the principal solutions of sin x − 1 = 0
Find the principal solutions of tan x = `-sqrt(3)`
`int 1/(sin x * cos x)` dx = ?
The general solution of sec θ = `sqrt2` is
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
The principal solutions of cot x = `sqrt3` are ______.
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
Which of the following equations has no solution?
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` 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 ______.
The number of principal solutions of tan 2θ = 1 is ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
If `2sin^-1 3/7` = cos–1β, then find the value of β.