Advertisements
Advertisements
Question
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Advertisements
Solution
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
RELATED QUESTIONS
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
tan θ = – 1
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
tan θ = - 1
Find the general solution of the following equation:
cos 4θ = cos 2θ
State whether the following equation has a solution or not?
2sinθ = 3
State whether the following equation have solution or not?
3 tanθ = 5
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:
If cos pθ = cos qθ, p ≠ q, then ______.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
`"cos"^-1 ("cos" (7pi)/6)` = _________.
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
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.
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
Find the principal solutions of cosec x = 2
Find the principal solutions of sin x − 1 = 0
The general solution of sec θ = `sqrt2` is
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) 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 ______
Which of the following is true in a triangle ABC?
The general solution of cot θ + tan θ = 2 is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ 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?
The general solution of the equation tan2 x = 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 ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
