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Question

If cos2A+cos2C=sin2B, then â–³ ABC is
[MP PET 1991]


A

Equilateral

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B

Right angled

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C

Isosceles

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D

None of these

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Solution

The correct option is B

Right angled


Trick: Obviously it is not an equilateral triangle because A=B=C=60o does not satisfy the given condition. But B = 90o then sin2 B = 1 and

cos2A+cos2C=cos2A+cos2(π2A)
=cos2A+sin2A=1
Hence this satisfy the condition, so it is a right angle triangle but not necessarily isosceles.


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