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if m=tana=sina and n=tana-sina then prove that m^2 -n^2 =4under root mn

if m=tana=sina and n=tana-sina then prove that m^2 -n^2 =4under root mn
 

Grade:11

1 Answers

Yarra Deva
39 Points
5 years ago
question has correction
m=tana+sina and n=tana -sina
m+n=2tana.m-n=2sina
(m+n)(m-n)=m^2-n^2=4tanasina
=4\sqrt{}tan^2asin^2a
=4\sqrt{}tan^2a(1-cos^2a)
=4\sqrt{}tan^2a-(sin^2acos^2a/cos^2a)
=4\sqrt{}tan^2a-sin^2a)
=4\sqrt{}(tana-sina)(tana+sina)
=4\sqrt{}mn
hence proved

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