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Answer 1 · 2017-11-28T12:49:33

Se the proof below (after modification)

I think that the identity to prove is

#cos^2theta-sin^2theta=(1-tan^2theta)/(1+tan^2theta)#

We need

#tan^2theta+1=sec^2theta#

#Tantheta=sintheta/costheta#

#sectheta=1/costheta#

Therefore,

#LHS=cos^2theta-sin^2theta#

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

#=(cos^2theta/cos^2theta-sin^2theta/cos^2theta)xx(1/sec^2theta)#

#=(1-tan^2theta)/sec^2theta#

#=(1-tan^2theta)/(1+tan^2theta)#

#=RHS#

#QED#