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Suppose A and B are two angles such that...

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____

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`cosA+cosB = 0`
`=>cosB = -cosA`
`=>cosB = cos(pi-A)`
`=>B = pi-A->(1)`
Now,
`sinA+sinB = 1`
`=>sinA+sin(pi-A) = 1`
`=>sinA+sinA = 1`
...
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