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Question

prove
tanA2tanB2+tanB2tanC2+tanC2tanA2=1

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Solution

A+B+C=πA+B+C2=π2A2+B2=π2C2

tan(A2+B2)=cotC2=1tanC2

tanA2+tanB21tanA2.tanB2=1tanC2

tanA2.tanC2+tanB2.tanC2=1tanA2.tanB2

tanA2.tanC2+tanB2.tanC2+tanA2.tanB2=1

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