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____

Options

A. 4
B. 6
C. 8
D. 12

Answer

C

Explanation

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`