Advertisements
Advertisements
प्रश्न
Solve the following equation for x:
tan−1`((1-x)/(1+x))-1/2` tan−1x = 0, where x > 0
उत्तर
tan−1`((1-x)/(1+x))-1/2` tan−1(x) = 0
⇒ `tan^-1((1-x)/(1+x))=1/2tan^-1(x)`
⇒ `tan^-1 1-tan^-1x=1/2tan^-1(x)`
⇒ `tan^-1 1=3/2tan^-1(x)`
⇒ `pi/4=3/2tan^-1(x)`
⇒ `pi/6=tan^-1(x)`
⇒ `x=1/sqrt3`
APPEARS IN
संबंधित प्रश्न
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin3)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of cos−1 (cos 6).
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
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.
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
If α = \[\tan^{- 1} \left( \frac{\sqrt{3}x}{2y - x} \right), \beta = \tan^{- 1} \left( \frac{2x - y}{\sqrt{3}y} \right),\]
then α − β =
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
If tan−1 (cot θ) = 2 θ, then θ =
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
