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Question

If A+B+C=π then,tanA2tanB2+tanB2tanC2+tanC2tanA2 =


A

tanA2 . tanB2 . tanC2

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B

tanA2 + tanB2 + tanC2

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C

tanA2. tanB2 . tanC2

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D

1

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Solution

The correct option is D

1


Given A+B+C=π

All the terms are half angles

Dividing both sides by 2

A+B+C2=π2

A2 + B2 = π2 - C2

tan(A2 + B2) = tan(π2 - C2)

tanA2+tanB21tanA2.tanB2 = cotC2 = 1tanC2

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

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


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