Question

if 3x=secø and (3/x)=tanø then find the value of (x²-1/x²)​

Answer 1

3x=secø & (3/x)=tanø

so,

(3x + 3/x) = (secø + tanø)

=> (x + 1/x) = (secø + tanø)/3

and ,

(x - 1/x) = (secø - tanø)/3

now,

(x²-1/x²)

= (x + 1/x) (x - 2/x)

= (secø + tanø)/3 × (secø - tanø)/3

= (sec^2ø - tan^2ø)/9

= 1/9 (ans.)

[(sec^2ø - tan^2ø)=1]