Advertisements
Advertisements
Question
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Solution
We know that
cot-1 (cot θ) = θ, (0, π)
We have
`cot^-1(cot (9pi)/4)=cot^-1[cot(2pi+pi/4)]`
`=cot^-1(cot pi/4)`
`=pi/4`
APPEARS IN
RELATED QUESTIONS
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(sin (4pi)/3)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`tan{cos^-1(-7/25)}`
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`
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
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)`
Write the value of sin−1 (sin 1550°).
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).
Write the principal value of `sin^-1(-1/2)`
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
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
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
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
Find the domain of `sec^(-1)(3x-1)`.
The value of sin `["cos"^-1 (7/25)]` is ____________.
