Question

If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`

Answer 1

5`(x^2 - 1/(x^2))`

=`25/5 ( x^2 -1/(x^2))`

=`1/5 (25x^2 - 25/(x^2))`

=`1/5 [ (5x)^2 - (5/x)^2]`

=`1/5 [(sec theta )^2 - ( tan theta )^2 ]`

=`1/5 (sec^2 theta - tan^2 theta)`

=`1/5 (1)`

=`1/5`

Answer 2

Given:

5x = sec θ, `5/x` = tan θ

⇒ sec θ = 5x, tan θ = `5/x`

We know that,

⇒ `(5x)^2 - (5/x)^2 = 1`

⇒ `25x^2 - 25/x^2 = 1`

⇒ `25 (x^2 - 1/x^2)=1`

⇒ `5 xx 5 xx (x^2 - 1/x^2)=1`

⇒ `5(x^2 - 1/x^2)`

⇒ `1/5`