SOLUTION: Let α & β be acute angles such that tan α=7 and sin β=4/5. Prove that α+β = 3/4π Hint: Consider cos(α+β)

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Question 795486: Let α & β be acute angles such that tan α=7 and sin β=4/5. Prove that α+β = 3/4π
Hint: Consider cos(α+β)
Answer by lwsshak3(11628) About Me  (Show Source):
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Let α & β be acute angles such that tan α=7 and sin β=4/5. Prove that α+β = 3/4π
Hint: Consider cos(α+β)
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Identity: tan(a+b)=(tan(a)+tan(b))/1-tan(a)*tan(b)
tan(a)=7
sin(b)=4/5 (3-4-5 right triangle)
cos(b)=3/5
tan(b)=sin(b)/cos(b)=4/3
tan(a+b)=((7+(4/3))/1-7*4/3
=(25/3)/1-(28/3)
=(25/3)/-(25/3)
=-1
tan(a+b)=-1
(a+b)=3π/4 (in quadrant II where tan<0)