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#