How do you simplify the expression $\frac{{sec}^{3} x - sec x}{5 sec x}$ $(sec^3x-secx)/(5secx)$ ?

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Answer 1 · 2016-10-14T16:31:32

Please the explanation for the process

Answer: $\frac{1}{5} {tan}^{2} (x)$ $1/5tan^2(x)$

Remove a common factor of $sec (x)$ $sec(x)$ from the numerator, because we know that $\frac{sec (x)}{sec (x)} = 1$ $sec(x)/sec(x) = 1$ :

$\frac{sec (x) ({sec}^{2} (x) - 1)}{5 sec (x)} = \frac{1}{5} ({sec}^{2} (x) - 1)$ $(sec(x)(sec^2(x) - 1))/(5sec(x)) = 1/5(sec^2(x) - 1)$

Substitute ${tan}^{2} (x)$ $tan^2(x)$ for $({sec}^{2} (x) - 1)$ $(sec^2(x) - 1)$ :

$\frac{1}{5} {tan}^{2} (x)$ $1/5tan^2(x)$

How do you simplify the expression (sec^3x-secx)/(5secx)sec3x−secx5secx(sec^3x-secx)/(5secx)?