1.

Suppose A and B are two angles such that `A , B in (0,pi)`and satisfy `sinA+sinB=1`and `cosA+cosB=0.`Then the value of `12cos2A+4cos2B`is____A. 4B. 6C. 8D. 12

Answer» Correct Answer - C
Since cos A + cos B = 0
`rArr A+B=pi`
`therefore B = pi -A`
`therefore` from sin A + sin B = 1
`sin A + sin(pi -A)=1`
`rArr sin A =(1)/(2)`
`therefore A=30^(@)` and `B=150^(@)`
or `A=150^(@)` and `B = 30^(@)`
`therefore 12 cos 60^(@)+4cos 300^(@)=8`


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