Advertisements
Advertisements
Question
Evaluate the following:
`cos^-1(cos3)`
Advertisements
Solution
We know
`cos^-1(costheta)=thetaif 0<=theta<=pi`
We have
`cos^-1(cos3)=3`
APPEARS IN
RELATED QUESTIONS
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
`sin^-1(sin (13pi)/7)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`sin(cos^-1 5/13)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
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:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
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`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
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 \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
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 : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
The period of the function f(x) = tan3x is ____________.
