Question #da28a

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Answer 1 · 2017-04-07T01:25:36

See below.

We know that $1-sin^2x=cos^2x$ . This comes handy later.

$8/(1-sinx)+8/(1+sinx)$

We can take out an $8$ from both fractions.
Multiply by the common denominators, and then add the two fractions.

$8/(1-sinx)(1+sinx)+\frac(8)(1+sinx)(1-sinx)$

$8(\frac(1+sinx)(1-sin^2)+\frac(1-sinx)(1-sin^2))$

$=8(\frac(2)(cos^2))$

$=16/cos^2x$

$=16sec^2x$