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From the Pythagorean identity, sin2x = 1-cos2x.

LHS = 1/(sinx cosx) - cosx/sinx

LHS = 1/(sinx cosx) - (cosx/sinx)(cosx/cosx)

LHS = 1/(sinx cosx) - cos2x/(sinx cosx)

LHS = (1- cos2x)/(sinx cosx)

LHS = sin2x /(sinx cosx) [from Pythagorean identity]

LHS = sin2x /(sinx cosx)

LHS = sinx/cosx

LHS = tanx [by definition]

RHS = tanx

LHS = RHS and so the identity is proven.

Q.E.D.

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โˆ™ 2011-03-27 22:07:03
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