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

1 Answer
Shwetank Mauria
Apr 24, 2017

#sintheta/(1+sintheta)-sintheta/(1-sintheta)=-2cot^2theta#

Explanation:

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

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

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

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

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

= #-2cot^2theta#

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