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If sin 2 a= 4 sin 2b, show that 5 tan(a-b)=3(tan a+b)

If sin 2 a= 4 sin 2b, show that 5 tan(a-b)=3(tan a+b)

Grade:11

1 Answers

Vikas TU
14149 Points
6 years ago
I think in RHs it is 3tan(a+b)

This can be solved by using componendo and dividendo.
 
sin 2a = 4 sin 2b (GIVEN)
then,
= > sin 2a / sin 2b = 4/1 
Apply Componendo – Dividendo, 

( sin 2a + sin 2b ) / ( sin 2a - sin 2b ) = (4+1)/(4-1) 
 { 2 sin (a+ b). cos (a- b) } / { 2 cos (a+ b). sin (a- b) } = 5/3 
 tan (a+ b) / tan (a- b) = 5/3 

5 tan (a- b) = 3 tan (a+ b)

Hence, Proved.

 

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