Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
4sin2θ = 1.
Advertisements
उत्तर
The general solution of sin2θ = sin2α is
θ = nπ ± α, n ∈ Z.
Now, 4 sin2θ = 1
∴ sin2θ = `1/4 = (1/2)^2`
∴ sin2θ = `(sin pi/6)^2 ...[∵ sin pi/(6) = (1)/(2)]`
∴ sin2θ = sin2 `pi/(6)`
∴ the required general solution is θ = nπ ± `pi/(6)`, n ∈ Z.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
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:
tan `(2θ)/(3) = sqrt3`
Find the general solution of the following equation:
sin θ = tan θ
State whether the following equation have solution or not?
cos 2θ = – 1
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)`.
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
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:
The principal solutions of equation cot θ = `sqrt3` are ______.
If `sqrt3`cos x - sin x = 1, then general value of x is ______.
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
The principal value of sin–1 `(- sqrt3/2)` is ______.
The principal value branch of sec-1x is ______.
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 principal solutions of the following equation:
cot θ = 0
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
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`.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
If | x | < 1, then prove that
`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`
Find the principal solutions of tan x = `-sqrt(3)`
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`int 1/(sin x * cos x)` dx = ?
The general solution of sec θ = `sqrt2` is
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
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 ______
If sin θ + cos θ = 1, then the general value of θ is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
Which of the following equation has no solution?
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 to cos100x – sin100x = 1 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
