Advertisements
Advertisements
प्रश्न
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Advertisements
उत्तर
We know that
\[\cot^{- 1} \left( - x \right) = \pi - \cot^{- 1} \left( x \right)\] Therefore, the value of \[\cot^{- 1} \left( - x \right)\] for all `x in R` in terms of `cot^-1(x)` is `pi-cot^-1(x)`
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.
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin12)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
`tan^-1 2/3=1/2tan^-1 12/5`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
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.`
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of cos−1 (cos 6).
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the principal value of `sin^-1(-1/2)`
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\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
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 =
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
If tan−1 (cot θ) = 2 θ, then θ =
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
