SOLUTION: Prove the following identity: (sin(2b))/(1-cos(2b))=1/(tan(b))

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Question 1114877: Prove the following identity:
(sin(2b))/(1-cos(2b))=1/(tan(b))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
(sin%282b%29%29%2F%281-cos%282b%29%29=1%2F%28tan%28b%29%29

start with left side and prove it is equal to right side:

%28sin%282b%29%29%2F%281-cos%282b%29%29.....since sin%282b%29=2sin%28b%29cos%28b%29+,and cos%282b%29+=+cos%5E2%28b%29+-+sin%5E2%28b%29+=+1+-2+sin%5E2%28b%29+=+2+cos%5E2%28b%29+-+1, we have

=%282sin%28b%29cos%28b%29%29%2F%281-%282+cos%5E2%28b%29+-+1%29%29

=%282sin%28b%29cos%28b%29%29%2F%281-2+cos%5E2%28b%29+%2B1%29

=%282sin%28b%29cos%28b%29%29%2F%282-2+cos%5E2%28b%29+%29

=%282sin%28b%29cos%28b%29%29%2F2%281-cos%5E2%28b%29+%29

=%28cross%282%29sin%28b%29cos%28b%29%29%2Fcross%282%29%281-cos%5E2%28b%29+%29

=%28sin%28b%29cos%28b%29%29%2F%281-cos%5E2%28b%29+%29.....since 1-cos%5E2%28b%29=+sin%5E2%28b%29 we have

= %28sin%28b%29+cos%28b%29%29%2F+sin%5E2%28b%29

= %28cross%28sin%28b%29%29+cos%28b%29%29%2F+sin%5Ecross%282%29%28b%29

= cos%28b%29%2F+sin%28b%29

= ctg%28b%29 ->=1%2Ftan%28b%29