Advertisements
Advertisements
Question
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Advertisements
Solution
We know
`cos^-1(costheta)=thetaif 0<=theta<=pi`
We have
`cos^-1{cos ((4pi)/3)}=cos^-1{cos(2pi-(2pi)/3)}`
`=cos^-1{cos((2pi)/3)}`
`=(2pi)/3`
APPEARS IN
RELATED QUESTIONS
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of 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 `f(x) =2cos^-1 2x+sin^-1x.`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate the following:
`cot(cos^-1 3/5)`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`tan^-1x+2cot^-1x=(2x)/3`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
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))`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
Find the domain of `sec^(-1) x-tan^(-1)x`
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
