Advertisements
Advertisements
Question
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Advertisements
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
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`
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the domain of `f(x)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin (17pi)/8)`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Evaluate the following:
`tan(cos^-1 8/17)`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Solve the following equation for x:
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
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:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of sin−1 (sin 1550°).
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)`
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
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 3 + tan−1 x = tan−1 8, then x =
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
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
The period of the function f(x) = tan3x is ____________.
Find the value of `sin^-1(cos((33π)/5))`.
