Advertisements
Advertisements
Question
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Advertisements
Solution
sin-1(1 - x) - 2 sin-1x = `pi/2`
∴ sin-1(1 - x) = `pi/2 + 2 sin^-1 "x"`
∴ 1 - x = sin `(pi/2 + 2 sin^-1"x")`
∴ 1 - x = cos (2 sin-1x) ....`[ ∵ sin (pi/2 + theta) = cos theta]`
∴ 1 - x = 1 - 2[sin(sin-1 x)]2 ....[∵ cos 2θ = 1 - 2 sin2θ]
∴ 1 - x = 1 - 2x2
∴ 2x2 - x = 0
∴ x(2x - 1) = 0
∴ x = 0 or x = `1/2`
When x = `1/2`
LHS = `sin^-1 (1 - 1/2) - 2 sin^-1 (1/2)`
`= sin^-1 (1/2) - 2 sin^-1 (1/2)`
`= - sin^-1 (1/2)`
`= - sin^-1 (sin pi/6)`
`= - pi/6 ne pi/2`
∴ `"x" ne 1/2`
Hence, x = 0.
APPEARS IN
RELATED QUESTIONS
Find the principal 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:
4 cos2 θ = 3
Find the general solution of the following equation:
4sin2θ = 1.
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:
The general solution of sec x = `sqrt(2)` is ______.
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
The principal value branch of sec-1x is ______.
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
Find the principal solutions of the following equation:
tan 3θ = - 1
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.
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Find the principal solutions of cosec x = 2
Find the principal solutions of cos 2𝑥 = 1
Find the principal solutions of sin x = `-1/2`
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 ______.
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of sin 18° is ______.
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of cosec x = `-sqrt2` is ______
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
Which of the following equation has no solution?
The general solution of the equation tan2 x = 1 is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
If `2sin^-1 3/7` = cos–1β, then find the value of β.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
If tan3θ = cotθ, then θ =
