Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Advertisements
उत्तर
The general solution of cos θ = cos α is
θ = 2nπ ± α, n ∈ Z
Now,
`cos θ = (sqrt(3))/(2) = cos (pi)/(6) ...[∵ cos pi/(6) = (sqrt(3))/(2)]`
∴ the required general solution is
θ = 2nπ ± `pi/(6)`, n ∈ Z.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
4sin2θ = 1.
Find the general solution of the following equation:
tan3θ = 3 tanθ.
In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
The principal value of sin–1 `(- sqrt3/2)` is ______.
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
The principal value branch of sec-1x 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
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`
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.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Prove the following:
`cos^-1 "x" = 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
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of cos 2𝑥 = 1
Find the principal solutions of sin x = `-1/2`
Find the principal solutions of tan x = `-sqrt(3)`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`int 1/(sin x * cos x)` dx = ?
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
The general solution of sec θ = `sqrt2` is
`int (sin (log x))^2/x` log x dx = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
The principal solutions of cot x = `sqrt3` are ______.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The general solution of 4sin2 x = 1 is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
Which of the following equation has no solution?
The number of principal solutions of tan 2θ = 1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
