Advertisements
Advertisements
प्रश्न
Write the function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
Advertisements
उत्तर
`tan^(-1) 1/(sqrt(x^2 - 1)`, |x| > 1
Put x = cosec θ ⇒ θ = cosec−1 x
`:. tan^(-1) 1/(sqrt(x^2 - 1)) = tan^(-1) 1/(sqrt(cosec^2 theta - 1))`
`= tan^(-1) (1/ cot theta) = tan^(-1) (tan theta)`
`= theta = cosec^(-1) x = pi/2 - sec^(-1) x`
`[cosec^(-1) x + sec^(-1) x = pi/2]`
APPEARS IN
संबंधित प्रश्न
If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
Prove that:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
Prove the following:
3 sin−1 x = sin−1 (3x − 4x3), `x ∈ [-1/2, 1/2]`
Write the following function in the simplest form:
`tan^(-1) (sqrt((1-cos x)/(1 + cos x)))`, 0 < x < π
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 < x < a/sqrt3`
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
Prove that:
`tan^(-1) sqrtx = 1/2 cos^(-1) (1-x)/(1+x)`, x ∈ [0, 1]
sin (tan–1 x), |x| < 1 is equal to ______.
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)`.
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Choose the correct alternative:
`sin^-1 3/5 - cos^-1 13/13 + sec^-1 5/3 - "cosec"^-1 13/12` is equal to
Choose the correct alternative:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
Choose the correct alternative:
If |x| ≤ 1, then `2tan^-1x - sin^-1 (2x)/(1 + x^2)` is equal to
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
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 the expression `tan (1/2 cos^-1 2/sqrt(5))` is ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
Solve for x : `"sin"^-1 2 "x" + sin^-1 3"x" = pi/3`
The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.
`"sin"^-1 ((-1)/2)`
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.
The value of `tan^-1 (x/y) - tan^-1 (x - y)/(x + y)` is equal to
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
If \[\tan^{-1}\left(\frac{x}{2}\right)+\tan^{-1}\left(\frac{y}{2}\right)+\tan^{-1}\left(\frac{z}{2}\right)=\frac{\pi}{2}\] then xy + yz + zx =
