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In triangle ABC if 2sin^(2)C=2+cos2A+cos...

In `triangle ABC` if `2sin^(2)C=2+cos2A+cos2B`, then prove that triangle is right angled.

Text Solution

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We have `2 sin^(2)C=2+cos2A+cos2B`
`therefore sin ^(2)A+sin^(2)B+sin^(2)C=2`
Now in `triangle ABC`,
`sin^(2)+sin^(2)B+sin^(2)C=2+2cos A cos B cos C`
`therefore sin A cos B cos C=theta`
Therefore, `triangle ABC`, must be righ angled triangle.
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