sin a+cos b=2/3
sin b+cos a=1/3
Find tan((a-b)/2)?
Note:Please give the shortest method....I know the longer one...
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2 Answers
36alternate... though not a short one..
(sina + cosb)(sinb + cosa) = 2/9
=> (cosa.cosb + sina.sinb) + (sina.cosa + sinb.cosb) = 2/9
=> cos(a - b) + sin(a+b)cos(a-b)= 2/9
=> cos(a - b)(1 + sin(a+b)) = 2/9
squaring and adding the two gives,
sin(a + b)
now, put cos(a - b) here,
tan{(a-b)/2} = {1 - cos(a-b)}/sin(a - b)
i admitted its not a 'shorter' one :)
