Question

If 5 x is equals to sec theta and 5 upon x is equal to 10 theta find 5( x square minus one upon x square).

Answer 1

sec²θ - tan²θ = 1
=> (5x)² - (5/x)² = 1
=> 25x² - 25/x² = 1
=> 25 ( x² - 1/x² ) = 1
=> 5 x 5 ( x² - 1/x² ) = 1
=> 5 x ( x² - 1/x² ) = 1/5.

Answer 2

As I lack symbol theta I am using A as theta
5x = sec A
=>x = secA/5

5/x = tanA
=>1/x = tanA/5

5(x²-1/x²)
=5(sec²A/5²- tan²A/5²)
=5(1/25)[Since, tan²A - sec²A=1]
=1/5