For a gt 0, t in (0, (pi)/(2)). Let x= s...

For `a gt 0, t in (0, (pi)/(2))`. Let `x= sqrt(a^(sin^(-1)t)) and y= sqrt(a^(cos^(-1)t)),` then `1+((dy)/(dx))^(2)` equals.

A

`(x^(2))/(y^(2))`

B

`(y^(2))/(x^(2))`

C

`(x^(2)+y^(2))/(y^(2))`

D

`(x^(2)+y^(2))/(x^(2))`

Verified by Experts

The correct Answer is:

D

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