Advertisements
Advertisements
Question
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
Advertisements
Solution
`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
RELATED QUESTIONS
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`
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`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
`sin^-1(sin2)`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`cos(tan^-1 3/4)`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
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))`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Write the range of tan−1 x.
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
If tan−1 3 + tan−1 x = tan−1 8, then x =
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
The period of the function f(x) = tan3x is ____________.
The value of sin `["cos"^-1 (7/25)]` is ____________.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
