Question #da28a

1 Answer
Apr 7, 2017

See below.

Explanation:

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#