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If cos^(2)A+cos^(2)B+cos^(2)C=1, then tr...

If `cos^(2)A+cos^(2)B+cos^(2)C=1`, then `triangle ABC` is

A

equilateral

B

isosceles

C

right angled

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
C
We have `cos^(2)A+cos^(2)B-(1-cos^(2)C)=0`
or `cos^(2)A+cos^(2)B-sin^(2)C=0`
or `cos^(2)A+cos(B+C)cos(B-C)=0`
or `cosA(cos(B+C)+cos(B-C)=0`
Hence, either `A` or B or C is `90^(@)`.
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