If 2\sin A=\sin(A-B) Prove that, \tan(A-B)=\frac{2\sin B}{1-2\cos B}

abiejose55d

abiejose55d

Answered question

2022-04-21

If 2sinA=sin(AB)
Prove that, tan(AB)=2sinB12cosB

Answer & Explanation

belamontern9i

belamontern9i

Beginner2022-04-22Added 19 answers

Since
2sin(A)=sin(A)cos(B)cos(A)sin(B)
sin(A)(cos(B)2)
=cos(A)sin(B)
we have
tan(AB)=sin(AB)cos(AB)
=2sin(A)cos(A)cos(B)+sin(A)sin(B)
=2sin(A)sin(A)(cos(B)2)cot(B)+sin(A)sin(B)
=2(cos(B)2)cot(B)+sin(B)
=2sin(B)(cos(B)2)cos(B)+sin2(B)
=2sin(B)12cos(B)

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