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____

Answer

8

Explanation

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