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Question

Prove that tanα=sin2α1+cos2α and hece deduce the values of tan15oand tan2212o

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Solution

sin2α1+cos2α=sin2αsin2α+cos2α+cos2αsin2α

=2sinαcosα2cos2α=tanα

tan15=sin2(15)1+cos2(15)=sin301+cos30=12+3

tan2212=sin451+cos45=11+2

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