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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