Advertisements
Advertisements
प्रश्न
sin–1 (1 – x) – 2 sin–1 x = `pi/2` , then x is equal to ______.
पर्याय
`0, 1/2`
`1, 1/2`
0
`1/2`
उत्तर
sin–1 (1 – x) – 2 sin–1 x = `pi/2` , then x is equal to 0.
Explanation:
`sin^-1 (1 - x) - 2sin^-1 x = pi/2`
= `sin^-1 (1 - x) = pi/2 + 2 sin^-1 x`
= `1 - x = cos [cos^-1 (1 - 2x^2)]`
= `1 - x = 1- 2x^2`
= `2x^2 - x = 0`
= `x = 0, 1/2`
But `x = 1/2` does not satisfy the equation so, x = 0.
APPEARS IN
संबंधित प्रश्न
If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.
Prove that `tan^(-1)((6x-8x^3)/(1-12x^2))-tan^(-1)((4x)/(1-4x^2))=tan^(-1)2x;|2x|<1/sqrt3`
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
sin (tan–1 x), | x| < 1 is equal to ______.
Solve for x : \[\tan^{- 1} \left( \frac{x - 2}{x - 1} \right) + \tan^{- 1} \left( \frac{x + 2}{x + 1} \right) = \frac{\pi}{4}\] .
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
If tan-1 x - cot-1 x = tan-1 `(1/sqrt(3)),`x> 0 then find the value of x and hence find the value of sec-1 `(2/x)`.
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`
Solve: `tan^-1x = cos^-1 (1 - "a"^2)/(1 + "a"^2) - cos^-1 (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`
Choose the correct alternative:
If `sin^-1x + cot^-1 (1/2) = pi/2`, then x is equal to
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
Evaluate `tan^-1(sin((-pi)/2))`.
Evaluate tan (tan–1(– 4)).
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
If a1, a2, a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression.
`tan[tan^-1("d"/(1 + "a"_1 "a"_2)) + tan^-1("d"/(21 + "a"_2 "a"_3)) + tan^-1("d"/(1 + "a"_3 "a"_4)) + ... + tan^-1("d"/(1 + "a"_("n" - 1) "a""n"))]`
If 3 tan–1x + cot–1x = π, then x equals ______.
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
The minimum value of sinx - cosx is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.
The value of sin (2tan-1 (0.75)) is equal to ____________.
The value of expression 2 `"sec"^-1 2 + "sin"^-1 (1/2)`
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
`"sin"^-1 (1/sqrt2)`
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
Measure of ∠EAB = ________.
`tan^-1 1/2 + tan^-1 2/11` is equal to
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
`tan(2tan^-1 1/5 + sec^-1 sqrt(5)/2 + 2tan^-1 1/8)` is equal to ______.
The set of all values of k for which (tan–1 x)3 + (cot–1 x)3 = kπ3, x ∈ R, is the internal ______.
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
