Advertisements
Advertisements
प्रश्न
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
उत्तर
We know that
cot-1 (cot θ) = θ, (0, π)
We have
`cot^-1{cot -((8pi)/3)}=cot^-1[-cot((8pi)/3)]`
`=cot^-1[-cot(3pi-pi/3)]`
`=cot^-1(cot pi/3)`
`=pi/3`
APPEARS IN
संबंधित प्रश्न
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Prove that
`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin3)`
`sin^-1(sin4)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Write the following in the simplest form:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate:
`tan{cos^-1(-7/25)}`
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of cos−1 (cos 1540°).
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
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)`
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
If tan−1 (cot θ) = 2 θ, then θ =
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
tanx is periodic with period ____________.
The period of the function f(x) = tan3x is ____________.
Find the value of `sin^-1(cos((33π)/5))`.
