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## Answers

So we need to prove that (tanФ-cotФ)/sinФcosФ=tan²Ф-cot²Ф

we can see that (tanФ-cotФ)/sinФcosФ=(tanФ-cotФ)(tanФ+cotФ)

So what we really need to prove is that 1/sinФcosФ=(tanФ+cotФ)

Now we know that (tanФ+cotФ)=sinФ/cosФ + cosФ/sinФ

or,(sin²Ф+cos²Ф)/(sinФcosФ)=(tanФ+cotФ)

[We know the fact that sin²Ф+cos²Ф=1] hence we have proved that 1/sinФcosФ=(tanФ+cotФ).Thus the problem is solved.

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