Advertisements
Advertisements
प्रश्न
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Advertisements
उत्तर
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
`=>cos^-1((1-x^2)/(1+x^2))+1/2xx2tan^-1x=(2x)/3` `[becausetan^-1((2x)/(1-x^2))=2tan^-1x]`
`=>2tan^-1x+tan^-1x=(2x)/3` `[becausecot^-1((1-x^2)/(1+x^2))=2tan^-1x]`
`=>3tan^-1x=(2x)/3`
`=>tan^-1x=(2x)/9`
`=>x=tan((2x)/9)`
APPEARS IN
संबंधित प्रश्न
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`cos(tan^-1 3/4)`
`tan^-1x+2cot^-1x=(2x)/3`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
If sin−1 x − cos−1 x = `pi/6` , then x =
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
Find the domain of `sec^(-1)(3x-1)`.
The value of sin `["cos"^-1 (7/25)]` is ____________.
