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

If `A+B=C,` then
`cos^(2)A+cos^(2)B+cos^(2)C-2cosAcosBcosC=`

A

1

B

2

C

0

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
`cos^(2)A+Cos^(2)B+cos^(2)C`
`=(1+cos2A)/(2)+(1+cos2B)/(2)+cos^(2)C`
`=1+(1)/(2)(cos2A+cos2B)+cos^(2)C`
`=1+(2)/(2)[cos(A+B)cos(A-B)]+cos^(2)C`
`=1+cosCcos(A-B)+cosCcos(A+B)`
`=1+cosC[cos(A-B)+cos(A+B)]`
`=1+2cosCcosBcosA`
`impliescos^(2)A+cos^(2)B+cos^(2)C-2cosAcosBcosC=1`
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