Advertisements
Advertisements
Question
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Options
`0, 1/2`
`1, 1/2`
0
`1/2`
Advertisements
Solution
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to 0.
Explanation:
sin–1 (1 – x) – 2 sin–1 x = `pi/2`
⇒ sin–1 (1 – x) = `pi/2 + 2 sin^-1 x`
⇒ 1 − x = cos[cos−1 (1 − 2x2)]
⇒ 1 − x = 1 − 2x2
⇒ 2x2 − x = 0
⇒ x = `0, 1/2`
But x = `1/2` does not satisfy the equation, so x = 0.
APPEARS IN
RELATED QUESTIONS
Prove that:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
Prove the following:
3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`
Write the following function in the simplest form:
`tan^(-1) (sqrt((1-cos x)/(1 + cos x)))`, 0 < x < π
Find the value of the following:
`tan 1/2 [sin^(-1) (2x)/(1+ x^2) + cos^(-1) (1-y^2)/(1+y^2)]`, |x| < 1, y > 0 and xy < 1
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
Prove `tan^(-1) 1/5 + tan^(-1) (1/7) + tan^(-1) 1/3 + tan^(-1) 1/8 = pi/4`
sin (tan–1 x), |x| < 1 is equal to ______.
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
Find the value, if it exists. If not, give the reason for non-existence
`tan^-1(sin(- (5pi)/2))`
Find the value of the expression in terms of x, with the help of a reference triangle
cos (tan–1 (3x – 1))
Prove that `tan^-1x + tan^-1y + tan^-1z = tan^-1[(x + y + z - xyz)/(1 - xy - yz - zx)]`
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
sin–1(2 cos2x – 1) + cos–1(1 – 2 sin2x) =
Evaluate `cos[sin^-1 1/4 + sec^-1 4/3]`
Prove that cot–17 + cot–18 + cot–118 = cot–13
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
If 3 tan–1x + cot–1x = π, then x equals ______.
If `sin^-1 ((2"a")/(1 + "a"^2)) + cos^-1 ((1 - "a"^2)/(1 + "a"^2)) = tan^-1 ((2x)/(1 - x^2))`. where a, x ∈ ] 0, 1, then the value of x is ______.
The value of cos215° - cos230° + cos245° - cos260° + cos275° is ______.
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
Solve for x : `"sin"^-1 2"x" + "sin"^-1 3"x" = pi/3`
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
If `"tan"^-1 2 "x + tan"^-1 3 "x" = pi/4`, then x is ____________.
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
