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`"If" tanA =(1-cosB)/(sinB), "then "tan2A =tanB`

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Given that, `" "tanA=(1-cosB)/(sinB)=(1-1+2sin^(2)""(B)/(2))/(2sin""(B)/(2)*cos""(B)/(2))=tan""(B)/(2)`
Now, `" "tan2A=(2tanA)/(1-tan^(2)A)=(2*tan""(B)/(2))/(1-tan^(2)""(B)/(2))=tanB`

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