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Prove that (i).(sin 2x)/(1-cos 2x) = c...

Prove that
`(i).(sin 2x)/(1-cos 2x) = cot x" " (ii) .(1- cos 2x)/(1+ cos 2x) = tan^(2) x`

Text Solution

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`(i) LHS = (sin 2x)/(1-cos 2x)`
`=(2sin x cos x)/(2 sin^(2) x)`
`[ :'` sin 2 x=2 sin x cos x , (1 - cos 2x) = 2 `sin^(2) x]`
= cot x = RHS
`" Hence " , (sin 2x)/(1- cos 2x) = cot x`
(ii) `LHS = (1- cos 2x)/(1+ cos 2x) = (2 sin^(2) x)/( 2 cos^(2) x) `
`= tan^(2) x = RHS`
`" Hence " , (1 - cos 2x)/(1+ cos 2x) = tan^(2) x`
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