Advertisements
Advertisements
Question
Find the general solution of the following equation:
4sin2θ = 1.
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:
Sec θ = `(2)/sqrt(3)`
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
cosθ + sinθ = 1.
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
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:
cot θ = 0
Find the general solutions of the following equation:
sin θ - cos θ = 1
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 2 tan-1(cos x) = tan-1(2 cosec x), 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`
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`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
Which of the following equations has no solution?
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The value of sin 18° is ______.
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general solution of cosec x = `-sqrt2` is ______
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
The general solution of cot 4x = –1 is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
