prove (tan(x)-cot(x))/(tan(x)+cot(x))=2sin^2(x)-1

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prove tan(x)−cot(x)tan(x)+cot(x) =2sin²(x)−1

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tan(x)−cot(x)tan(x)+cot(x) =2sin²(x)−1

Manipulating left side

tan(x)−cot(x)tan(x)+cot(x)

Express with sin, cos

=−cos²(x)+sin²(x)cos²(x)+sin²(x)

Rewrite using trig identities

=−1+2sin²(x)

=2sin²(x)−1

We showed that the two sides could take the same form

⇒ True

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prove (tan(x)-cot(x))/(tan(x)+cot(x))=2sin^2(x)-1

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