If 5k = tan θ and $\frac{5}{k} = secθ$, then what is the value of $10(k^2-\frac{1}{k^2})$ ?
Answer & explanation
Correct answer: option 3
tan θ = 5k
\(\frac{tan θ }{5}\) = k
& \(\frac{5 }{k}\) = sec θ
\(\frac{1 }{k}\) = \(\frac{sec θ }{5}\)
Now,
10 ( k² - \(\frac{1 }{k²}\) )
= 10 ( (\(\frac{tan θ }{5}\))² - (\(\frac{sec θ }{5}\))² )
= 10 ( (\(\frac{tan² θ }{25}\)) - (\(\frac{sec² θ }{25}\)) )
{ we know, sec² θ - tan² θ = 1 }
= -\(\frac{2 }{5}\)