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The value of cos [tan^-1 {sin (cot^-1 x)...

The value of `cos [tan^-1 {sin (cot^-1 x)}]` is

A

`sqrt(x^(2)+2)/(x^(2)+3)`

B

`sqrt(x^(2)+2)/(x^(2)+1)`

C

`sqrt(x^(2)+1)/(x^(2)+2)`

D

none of these

Text Solution

Verified by Experts

We have
`cos[tan^(-1) sin(cot(-1)x)]`
`cos{tan^(-1)(1)/sqrt(1+x^(2))}=sqrt(1+x^(2))/sqrt(2+x^(2))=sqrt(1+x^(2))=sqrt(1+x^(2))/(2+x^(2))`
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. If -1lexle0 then sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x...

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  2. If |cos^-1((1-x^2)/(1+x^2))| < pi/3, then x belongs to the interval

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  3. The value of cos [tan^-1 {sin (cot^-1 x)}] is

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  4. Find the value of sin^(-1)(cos(sin^(-1)x))+cos^(-1)(sin(cos^(-1)x))

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  5. If (sin^(-1)x)^(2)+(cos^(-1)x)^(2)=(5pi^(2))/(8) then x =

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  6. tan{(pi)/(4)+1/2cos^(-1)alpha}+tan{(pi)/(4)-1/2cos^(-1)alpha} alpha ...

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  7. The solution set of the equation cos^(-1)x-sin^(-1)x=sin^(-1)(1-x) i...

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  8. The number of triple satisfying sin^(-1)x+cos^(-1)y+sin^(-1)z=2pi is

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  9. If sin^-1(sin 5)gtx^(2)-4x then

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  10. If cos^(-1)(cos 4)gt3x^(2)-4x then

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  11. The number of real solution (x,y) where |y|=sinx,y=cos^(-1)(cosx),-2pi...

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  12. If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=

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  13. tan(sec^(-1)x )=sin(cos^(-1)(1/sqrt5))

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  14. Number of integral solutions of the equation 2 sin^-1sqrt(x^2-x +1 )+ ...

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  15. If alpha, beta and gamma are the three angles with alpha = 2tan^(-1)(s...

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  16. If f(x) =cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))} then f(2/3) equ...

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  17. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  18. If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = ...

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  19. If tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2) t...

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  20. If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=

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