If `sectheta=x+1/(4x)` , then `s e ctheta-t a ntheta` is equal to `-2x ,1/(2x)` b. `1/(2x),\ 2x` c. `2x` d. `2x ,1/(2x)`

Explanation

`tan ^{2} theta=sec ^{2} theta-1`

`=(x+frac{1}{4 x})^{2}-1`

`=(x+frac{1}{4 x})^{2}`

`therefore tan theta=pm(x-frac{1}{4 x})`

`=(x-frac{1}{4 x})` or `(frac{1}{4 x}-x)`

`therefore sec theta+tan theta` is either `2 x` or `frac{1}{2 x}`