Prove that cot theta-tan theta=2cot 2 th...

Prove that `cot theta-tan theta=2cot 2 theta`.

Text Solution

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`cot theta-tan theta=(cos theta)/(sin theta)-(sin theta)/(cos theta)`
`=(cos ^(2)theta-sin^(2)theta)/(sin theta cos theta)`
`=(2cos 2theta)/(sin 2theta)`
`=2cot 2 theta`.

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