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If sin B = sin (2A + B) /5 , then 2tan (A + B) / tan A =

If sin B = sin (2A + B) /5 , then 2tan (A + B) / tan A = 

Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
write this as:
sin (2A + B)/sin B = 5/1
apply componendo and dividendo
[sin (2A + B)+sin B]/[sin (2A + B) – sin B]= (5+1)/(5 – 1)
now apply sin x + sin y = 2 sin (x+y)/2 *cos (x−y)/2 and sin x – sin y = 2 sin (x-y)/2 *cos (x+y)/2 
2sin(A+B)cosA/2sinAcos(A+B)=6/4=3/2
tan(A+B)/tanA=3/2
or 2tan(A+B)/tanA = 3

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