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If sin3a=5sinb then find the value of tan [(a+b)/2] / tan[(a-b)/2]. Please explain with steps.

If sin3a=5sinb then find the value of tan [(a+b)/2] / tan[(a-b)/2]. Please explain with steps.

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear Purva
 
3sina=5sinb
rearranging it 
(sina/sinb)=(5/3)
now applying componendo and dividendo rule 
we get 
(sina+sinb)/(sina-sinb)=4
now using the identities of trigonometry we get 
(2sin((a+b)/2)cos((a-b)/2)  )/(  2cos((a+b)/2)sin((a-b)/2))=4
this becomes
(tan((a+b)/2)  )/( tan((a-b)/2)=4
 
 
Hope it helps
 
Regards
Arun (askIITians forum expert)

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