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Question
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
Options
25
`1/25`
5
1
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Solution
`1/25`
Explanation;
Hint:
5x = sec θ
x = `(sec theta/5)`
∴ x2 = `(sec^2 theta)/25`
`5/x` = tan θ
`1/x = tan theta/5`
`1/x^2 = (tan^2 theta)/25`
`x^2 - 1/x^2 = (sec^2 theta)/25 - (tan^2 theta)/25`
= `(sec^2 theta - tan^2 theta)/25`
= `1/25`
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