Can someone help me solve this trigonometric expression please? Thanks!

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1 Answer
Sep 23, 2017

The correct answer is #2sec^2theta#.

Explanation:

The obvious first step here would be to put on a common denominator.

#1/(1 + sintheta) + 1/(1 - sintheta)#

#=(1 -sintheta)/((1 + sintheta)(1 -sintheta)) + (1 + sintheta)/((1 - sintheta)(1+ sintheta))#

#= (1 - sintheta + 1 + sintheta)/((1 + sintheta)(1 - sintheta))#

#= 2/(1 - sin^2theta)#

We know that #sin^2x + cos^2x = 1#, therefore:

#= 2/cos^2theta#

#= 2sec^2theta#

Hopefully this helps!