Question 769552: tan α =15/8 , π < α <3pi/2 ; cos β = -21/29 , pi/2 < β < π Find tan (α + β).
a) 155/468
b) 468/493
c)-11/39
d) 155/493 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! tan α =15/8 , π < α <3pi/2 ; cos β = -21/29 , pi/2 < β < π Find tan (α + β)
use a for α
use b for β
..
tan(a+b)=(tan a+tan b)/(1-tan a* tan b)
cos b=-21/29
sin b=√(1-cos^2b)=√(1-(441/841))=√(400/841)=20/29
tan b=sin b/cos b=-20/21
tan(a+b)=(15/8-20/21)/(1-(15/8)*(-20/21))
tan(a+b)=(21*15-8*20)/168)/(1+300/168)
=((315-160)/168))/(468/168)
=155/168/(468/168)
=155/468
calculator check:
tan a=15/8
a=≈61.9275º
cos b=-21/29
b≈136.3972
a+b≈198.3247
tan(a+b)=tan(198.3247)≈0.3312..
Exact answer as calculated=155/468≈0.3312..
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