Grade 11Trigonometry
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)
1 Answer
Vikas TU
Approved Tutor Answer10 Years agoI 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.
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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