The algebraic expression for `f(x)=tan(sin^(-1)(cos("tan"^(-1)(x)/(2))))` isA. `(2)/(x)`B. `(x)/(2)`C. `(1)/(x)`D. `(2)/(|x|)`

The algebraic expression for `f(x)=tan(sin^(-1)(cos("tan"^(-1)(x)/(2))

1.	The algebraic expression for `f(x)=tan(sin^(-1)(cos("tan"^(-1)(x)/(2))))` isA. `(2)/(x)`B. `(x)/(2)`C. `(1)/(x)`D. `(2)/(\|x\|)`
Answer» Correct Answer - D Let `"tan"^(-1) (x)/(2)=theta` `rArr tan. theta=(x)/(2)` `rArr cos("tan"^(-1)(x)/(2))=cos. theta=(2)/(sqrt(4+x^(2)))` `rArr f(x)=tan["sin"^(-1)(2)/(sqrt(4+x^(2)))]=(2)/(x)` If `x gt 0`, then `f(x)=tan("tan"^(-1)(2)/(x))=(2)/(x)` If `x lt 0`, then `f(x)=tan(tan^(-1)((-2)/(x)))=(-2)/(x)` `rArr f(x)=(2)/(\|x\|)`

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