`tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a`

1.	`tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),\|x\|lt a`
Answer» `tan^(-1)""(x)/(sqrt(a^(2)-x^(2)))` `=tan^(-1)""(a sin theta)/(sqrt(a^(2)-a^(2) sin^(2)theta))` `=tan^(-1)""(a sin theta)/(sqrt(a^(2)(1-sin^(2)theta)))" " Let x=a sin theta implies sin theta =(x)/(a)implies theta=sin^(-1)""((x)/(a))` `=tan^(-1)""(a sin theta)/(sqrt(a^(2)cos^(2)theta))` `=tan^(-1)""(a sin theta)/(a cos theta)=tan^(-1)(tan theta)` `=theta=sin^(-1)""(x)/(a)`

Discussion

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