Advertisements
Advertisements
Question
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Advertisements
Solution
We know
\[\tan^{- 1} x + \cot^{- 1} x = \frac{\pi}{2}\]
\[\therefore \tan^{- 1} \sqrt{3} + \cot^{- 1} \sqrt{3} = \frac{\pi}{2}\]
APPEARS IN
RELATED QUESTIONS
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate:
`cot(tan^-1a+cot^-1a)`
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.
Solve the following equation for x:
`tan^-1 x/2+tan^-1 x/3=pi/4, 0<x<sqrt6`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
`tan^-1 2/3=1/2tan^-1 12/5`
If x < 0, then write the value of cos−1 `((1-x^2)/(1+x^2))` in terms of tan−1 x.
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of cos−1 (cos 6).
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
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
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
