Advertisements
Advertisements
प्रश्न
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Advertisements
उत्तर
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
`=>6tan^-1x-8tan^-1x+4tan^-1x=pi/3` `[because 2tan^-1x=sin^-1((2x)/(1+x^2)),2tan^-1x=cos^-1((1-x^2)/(1+x^2))and 2tan^-1x=tan^-1((2x)/(1-x^2))]`
`=>2tan^-1x=pi/3`
`=>tan^-1x=pi/6`
`=>x=tan pi/6`
`=>x=1/sqrt3`
APPEARS IN
संबंधित प्रश्न
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
Find the domain of `f(x)=cos^-1x+cosx.`
`sin^-1(sin (13pi)/7)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`tan{cos^-1(-7/25)}`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
`4sin^-1x=pi-cos^-1x`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of cos−1 (cos 1540°).
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
The set of values of `\text(cosec)^-1(sqrt3/2)`
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
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
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
Find the domain of `sec^(-1)(3x-1)`.
Find the domain of `sec^(-1) x-tan^(-1)x`
