1-tan square theta / 1+tan square theta =1-sin square theta ?

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Answer 1 · 2018-05-22T15:22:49

Please see the explanation below.

We need

#tantheta=sintheta/costheta#

#sin^2theta+cos^2theta=1#

Therefore,

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

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

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

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

#=1-2sin^2theta#

#=LHS#

#QED#

NB. I think there is a mistake in the subject.

Please check!!!!