Choose the correct answer in each of the following questions:
If `2x=sec A and (2)/(x)=tanA" then " 2(x^(2)-(1)/(x^(2)))=?`

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. `(1)/(8)`
D. `(1)/(16)`

Answer

A

Explanation

We know that `sec^(2)A-tan^(2)A=1.`
`therefore (2x)^(2)-((2)/(x))^(2)=1rArr4x^(2)-(4)/(x^(2))=1rArr4(x^(2)-(1)/(x^(2)))=1`
`rArr(x^(2)-(1)/(x^(2)))=(1)/(4)rArr2(x^(2)-(1)/(x^(2)))=2xx(1)/(4)=(1)/(2).`