Question

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tan(x)cot(x)=1

Answer 1

There are two ways to confirm the identity.

Method 1

`\tan(x)\cot(x) = 1\\\\\tan(x)(1)/(\tan(x)) = 1\\\\(\tan(x))/(\tan(x)) = 1\\\\1 = 1 \ \ \checkmark\\\\`

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Method 2

`\tan(x)\cot(x) = 1\\\\\left((\sin(x))/(\cos(x))\right)\left((\cos(x))/(\sin(x))\right) = 1\\\\(\sin(x)\cos(x))/(\cos(x)\sin(x)) = 1\\\\(\sin(x))/(\sin(x)) = 1\\\\1 = 1 \ \ \checkmark\\\\`