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

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prove cot(2x)=1−tan²(x)2tan(x)

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cot(2x)=1−tan²(x)2tan(x)

Manipulating right side

1−tan²(x)2tan(x)

Express with sin, cos

=cos²(x)−sin²(x)2cos(x)sin(x)

Rewrite using trig identities

=cos(2x)sin(2x)

Use the basic trigonometric identity: cos(x)sin(x) =cot(x)

=cot(2x)

We showed that the two sides could take the same form

⇒ True

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

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