Advertisements
Advertisements
प्रश्न
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Advertisements
उत्तर
We know
`tan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))`
`thereforetan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3`
`=>tan^-1((2x)/(1-x^2))+tan^-1((2x)/(1-x^2))=(2pi)/3` `[becausecot^1x=tan^-1 1/x]`
`=>tan^-1((2x)/(1-x^2))=pi/3`
`=>2tan^-1x=pi/3` `[because2tan^-1xtan^-1((2x)/(1-x^2))]`
`=>tan^-1x=pi/6`
`=>x=tan pi/6`
`=>x=1/sqrt3`
APPEARS IN
संबंधित प्रश्न
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
`sin^-1(sin (13pi)/7)`
`sin^-1(sin (17pi)/8)`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`sin(sin^-1 7/25)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
`4sin^-1x=pi-cos^-1x`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`tan^-1 2/3=1/2tan^-1 12/5`
If `sin^-1 (2a)/(1+a^2)-cos^-1 (1-b^2)/(1+b^2)=tan^-1 (2x)/(1-x^2)`, then prove that `x=(a-b)/(1+ab)`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Prove that:
`tan^-1 (2ab)/(a^2-b^2)+tan^-1 (2xy)/(x^2-y^2)=tan^-1 (2alphabeta)/(alpha^2-beta^2),` where `alpha=ax-by and beta=ay+bx.`
For any a, b, x, y > 0, prove that:
`2/3tan^-1((3ab^2-a^3)/(b^3-3a^2b))+2/3tan^-1((3xy^2-x^3)/(y^3-3x^2y))=tan^-1 (2alphabeta)/(alpha^2-beta^2)`
`where alpha =-ax+by, beta=bx+ay`
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
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 \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
tanx is periodic with period ____________.
