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

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

A

`pm (3)/sqrt(5)`

B

`pm sqrt(5)/(3)`

C

`pm sqrt(3/5)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`tan(sec^(-1)x)=sin(cos^(-1)(1)/sqrt(5))`
`rarr sqrt(sec^(2)(sec^(-1)x)-1)=sin(sin^(-1)(2)/sqrt(5))`
`rarr sqrt(x^(2)-1)=(2)/sqrt(5)rarrx=pm (3)/sqrt(5)`
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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  2. If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=

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

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

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

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

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

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

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  11. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then the value of xsqrt(1-x^(2))+y...

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  12. if cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4 ,the...

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  13. The solution set of the equation sin^(-1)x=2 tan^(-1)x is

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  14. If cot(cos^(-1)x)=sec{tan^(-1)((a)/sqrt(b^(2)-a^(2)))} then x equals

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  15. tan^(-1)(C(1)x-y)/(c(1)+c(3)c(2))+..+tan^(-1)(1)/(c(n)) is equal top

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  16. If 0ltxlt1 then sqrt(1+x^(2))[{x cos (cot^(-1)x)+sin(cot^(-1)x}^(2)-1...

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  19. Let f:[0,4pi]->[0,pi] be defined by f(x)=cos^-1(cos x). The number ...

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