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If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-...

If `alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)))` then prove that `x^(2) = sin 2alpha`.

A

`cos2alpha`

B

`tan2alpha`

C

`sin2alpha`

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
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  11. If Sin^(-1)(x//5)+Cosec^(-1)(5//4)=pi//2 then a value of x is

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  12. If Sin^(-1)x-Cos^(-1)x = (pi)/6 then find x.

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  13. If Sin^(-1)x+Sin^(-1)(1-x)=Cos^(-1)x then x =

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  14. The equation Sin^(-1)x-Cos^(-1)x=Cos^(-1)(sqrt3//2) has

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  15. If Tan^(-1)(x+1)+Tan^(-1)(x-1)=Tan^(-1)(4//7), then x =

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  16. A solution of the equation Tan^(-1)(1+x)+Tan^(-1)(1-x)=pi//2 is

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  19. tan(Cos^(-1)1//x)=sin(Cot^(-1)1//2),"if "xne0 then x =

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  20. The value of x where xgt0andtan(Sec^(-1)(1/x))=sin(Tan^(-1)2) is

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