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
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`
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
`4sin^-1x=pi-cos^-1x`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, 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`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Write the value of sin (cot−1 x).
Write the value of cos−1 (cos 1540°).
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
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 \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Find the domain of `sec^(-1) x-tan^(-1)x`
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
tanx is periodic with period ____________.
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
