Advertisements
Advertisements
प्रश्न
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
Advertisements
उत्तर
`sin(tan^-1x+tan^-1 1/x)`
`=sin(tan^-1x+cot^-1x)` `[thereforetan^-1x=cot^-1 1/x]`
`=sin(pi/2)` `[thereforetan^-1x=cot^-1x=pi/2]`
= 1
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin (5pi)/6)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`cosec(cos^-1 3/5)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Evaluate:
`tan{cos^-1(-7/25)}`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
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)`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
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 `sin^-1(-1/2)`
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] 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
If 4 cos−1 x + sin−1 x = π, then the value of x is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
The value of sin `["cos"^-1 (7/25)]` is ____________.
