Advertisements
Advertisements
Question
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
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
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin pi/6)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan2)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`cot(cos^-1 3/5)`
Evaluate:
`tan{cos^-1(-7/25)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`cot(tan^-1a+cot^-1a)`
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`tan^-1x+2cot^-1x=(2x)/3`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
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)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=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`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of cos−1 (cos 1540°).
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
If sin−1 x − cos−1 x = `pi/6` , then x =
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 =
If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
