Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cot^-1(cot (19pi)/6)`
उत्तर
We know that
cot-1 (cot θ) = θ, (0, π)
We have
`cot^-1(cot (19pi)/6)=cot^-1[cot(pi+pi/6)]`
`=cot^-1(cot pi/6)`
`=pi/6`
APPEARS IN
संबंधित प्रश्न
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
`sin^-1(sin pi/6)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`tan^-1(tan2)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`sin(cos^-1 5/13)`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Write the value of cos−1 (cos 6).
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the domain of `sec^(-1) x-tan^(-1)x`
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.