If 2x = sec A and 2/x = tan A then 2 (x^2 - 1/x^2) = ? ​

Question

If 2x = sec A and 2/x = tan A then 2\((x^2-\frac{1}{x^2})\) = ?

(a) 1/2

(b) 1/4 

(c) 1/8a

(d) 1/16

Answer 1

Correct answer is (a) 1/2

Given: 2x = sec A and 2/x = tan A

Also, we can deduce that x = sec A/2 and 1/x = tanA/2 

So, substituting the values of x and 1/x in the given expression, we get

= 2/4 (sec² A − tan² A) 

= 1/2 [By using the identity: (sec² θ − tan² θ = 1) ]