Question #cf9c7

1 Answer
sente
Sep 5, 2016

sec(x)csc(x) - sec(-x)csc(-x)=2sec(x)csc(x)

Explanation:

For this problem, we will make use of the facts that

-csc(-x) = -csc(x)
-sec(-x) = sec(x)

(these are due to sine being an odd function and cosine being an even function, together with the definitions of the secant and cosecant functions)

sec(x)csc(x) - sec(-x)csc(-x)

= sec(x)csc(x)-sec(x)(-csc(x))

=sec(x)csc(x)+sec(x)csc(x)

=2sec(x)csc(x)

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