Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Advertisements
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
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin (7pi)/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate the following:
`sec(sin^-1 12/13)`
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
`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)`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of cos−1 (cos 1540°).
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
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 value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
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) x-tan^(-1)x`
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
