Verify that sec(θ)/csc(θ)-cot(θ) - sec(θ)/csc(θ)-cot(θ) = 2csc(θ) is an identity.

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1 answer

sec(θ)/(csc(θ)-cot(θ)) - sec(θ)/(csc(θ)+cot(θ))
becomes

sec(θ)(csc(θ)+cot(θ)) - sec(θ)(csc(θ)-cot(θ))
----------------------------------------------------------
(csc(θ)-cot(θ))(csc(θ)+cot(θ))

Now expand the numerator and note that the denominator is just 1.
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