Advertisements
Advertisements
प्रश्न
Find the general solutions of the following equation:
`tan theta = - sqrt3`
उत्तर
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z.
Now, tan θ = - `sqrt3`
∴ tan θ = - `tan pi/3 ....[because "tan" pi/3 = sqrt3]`
∴ tan θ = tan`(pi - pi/3) ...[because tan (pi - theta) = - tan theta]`
∴ tan θ = tan`(2pi)/3`
∴ the required general solution is
∴ θ = `"n"pi + (2pi)/3,` n ∈ Z
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`.
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
cos2θ = – 1.
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 ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
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`
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
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 = 1/3 tan^-1 11/2`
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Find the principal solutions of cos 2𝑥 = 1
Find the principal solutions of tan x = `-sqrt(3)`
`int (sin (log x))^2/x` log x dx = ?
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
The principal solutions of cot x = `sqrt3` are ______.
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The general solution of 4sin2 x = 1 is ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
The number of principal solutions of tan 2θ = 1 is ______.
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 ______.
The general solution to cos100x – sin100x = 1 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
