Posted by Chelsie on Monday, June 13, 2011 at 9:29pm.
Given that sin alpha=4/sqrt65, pi/2<alpha<pi, and cos beta=3/sqrt13, tan beta>0, find the exact value of tan(alpha+beta)

Math  Reiny, Monday, June 13, 2011 at 9:52pm
I will use a for alpha and b for beta
sin a = 4/√65 , then cos a = 7/√65 in II
tana = sina/cosa = 4/7
cosb = 3/√13 , then sin b = 2/√13 in III
tanb = 2/3
tan(a+b) = (tana + tanb)/(1  tanatanb)
= (4/7 + 2/3)/(1  (4/7)(2/3))
= 2/29
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