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Prove that: (cosA+cosB)^(2)+(sinA+sinB...

Prove that:
`(cosA+cosB)^(2)+(sinA+sinB)^(2)=4cos^(2)(A-B)/2`

Text Solution

Verified by Experts

LHS `=(cosA+cosB)^(2)+(sinA+sinB)^(2)`
`=(2cos(A+B)/(2)cos^(2)(A+B)/(2)+sin^(2)(A+B)/(2))`
`=4 cos^(2)(A-B)/2(1)`
`=4 cos^(2)(A-B)/2` =RHS Hence Proved.
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