Advertisements
Advertisements
Question
Find the general solution of the following equation:
4sin2θ = 1.
Advertisements
Solution
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
RELATED QUESTIONS
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
cot θ = 0
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
sin θ = tan θ
Find the general solution of the following equation:
tan3θ = 3 tanθ.
Find the general solution of the following equation:
cosθ + sinθ = 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.
Select the correct option from the given alternatives:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
`"cos"^-1 ("cos" (7pi)/6)` = _________.
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Find the principal solutions of cosec x = 2
Find the principal solutions of sin x − 1 = 0
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`cos^-1 (cos (4pi)/3)` = ______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The general solution of sin 2x = cos 2x is ______
The general solution of 4sin2 x = 1 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?
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
The general solution to cos100x – sin100x = 1 is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
If tan3θ = cotθ, then θ =
