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The value of "tan"(sin^(-1)("cos"(sin^(-...

The value of `"tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(-1)x))),w h e r ex in (0,1),` is equal to 0 (b) 1 (c) `-1` (d) none of these

A

0

B

1

C

`-1`

D

none of these

Text Solution

Verified by Experts

we have
`cos(sin^(-1)x)=sqrt(1-x^(2)) and sin cos^(-1)x=sqrt(1-x^(2))`
`therefore tan{sin^(-1)(cos sin^(-1)x)}tan{cos^(-12)(sin(cos^(-1)x)}`
`=tan{sin^(-1)sqrt(1-x^(2))}tan{cos^(-1)sqrt(1-x^(2))`
`=tan(sin^(-1)sqrt(1-x^(2))tan{(pi)/(2)-sin^(-1)sqrt(1-x^(2))=1`
`=tan(sin^(-1)sqrt(1-x^(2))cot(sin^(-1))sqrt(1-x^(2))=1`
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  2. The number of solution of sin{sin^(-1)(log(1//2)x)}+2|cos{sin^(-1)(x...

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  3. The value of "tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(...

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  4. Value of x satisfying tan(sec^(- 1)x)=sin(cos^(- 1)(1/(sqrt(5))))

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  5. Exhaustive set of values of parameter 'a' so that sin^(-1)x-tan^(-1)x=...

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  6. If alpha le sin^(-1)x+cos^(1)x +tan^(-1)xlebeta then

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  7. If -1lexle0 then sin^(-1)x equals

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  8. If tan^(-1)((x+1)/(x-1))+tan^(-1)((x-1)/(x))=tan^(-1)(-7)+pi then x =

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  9. The value of tan^(-1)1/3+tan^(-1)1/7+tan^(-1)1/13+..+tan^(-1)(1)/(n^(...

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  10. If 0lexle1 then tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-x^(2))...

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  11. If -1lexle0 then tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-x^(2)...

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  12. If 0lexle1 then sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^...

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  13. If -1lexle0 then sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x...

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

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

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

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

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

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

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

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