If ` sec theta + tan theta =x` then ` sin theta` is equal to

Options

A. `(x^(2)+1)/(2x)`
B. `(x^(2) +1)/(x^(2)-1)`
C. `(x^(2) -1)/(x^(2)+1)`
D. `(2x)/(x^(2) -1)`

Answer

C

Explanation

we have, ` sec theta + tan theta =x`
` Rightarrow ( sec theta + tan theta) ( sec theta - tan theta) =x ( sec theta - tan theta)`
` Rightarrow sec theta - tan theta =1/x`
Adding Eqs. (i) and (ii) , we get
` 2 sec theta = x + 1/x`
Substracting Eqs. (ii) from (i) , we get
`2 tan theta x-1/x`
` (2 tan theta)/( 2 sec theta) = ( x-1/x)/( x+ 1/x)`
` Rightarrow sin theta = (x^(2) -1)/(x^(2) +1)`