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