Advertisements
Advertisements
प्रश्न
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Advertisements
उत्तर
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
संबंधित प्रश्न
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 principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
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:
sin 2θ = `1/2`
Find the general solution of the following equation:
cot 4θ = – 1
State whether the following equation have solution or not?
cos 2θ = – 1
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
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:
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 ______.
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
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 general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
`tan^2 theta = 3`
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`
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/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 tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
If x, y, z are positive, then prove that
`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`cos^-1 (cos (4pi)/3)` = ______.
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
`int (sin (log x))^2/x` log x dx = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The principal solutions of cot x = `sqrt3` are ______.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The value of sin 18° is ______.
The general solution of 4sin2 x = 1 is ______.
The general solution of cosec x = `-sqrt2` is ______
Find the principal solutions of cot θ = 0
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
The general solution to cos100x – sin100x = 1 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 ______.
