Tan teta - cot teta =2sin 2 teta -1/sin teta * cos teta
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tanα - cotα = (2sin²α -1)/(sinα cosα)
LHS
(sinα/cosα) - (cosα/sinα)
=(sin²α - cos²α)/(sinαcosα)
=[sin²α -(1-sin²α) ]/(sinαcosα)
=[sin²α-1 +sin²α]/(sinαcosα)
=(2sin²α-1)/(sinαcosα)
=RHS
LHS
(sinα/cosα) - (cosα/sinα)
=(sin²α - cos²α)/(sinαcosα)
=[sin²α -(1-sin²α) ]/(sinαcosα)
=[sin²α-1 +sin²α]/(sinαcosα)
=(2sin²α-1)/(sinαcosα)
=RHS
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