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Question

If A+B+C=π and cosA=cosB.cosC then show that cotB cotC=12.

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Solution

Let us consider the problem.
Let A+B+C=1800 degrees
Hence
A=1800(B+C)
Therefore
cosA=cosB+cosC
Implies that
cos(1800BC)=cosBcosC
implies that
cos(B+C)=cosB.cosC
Implies that
cosBcosC+sinBsinC=cosB.cosC
Implies that
2cosBcosC=sinBsinC
Implies that
Hence cotBcotC=12

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