Question

Please help i don't know what I'm doing!!! :( multiply and simplify cot x( sin x - sec x)

Answer 1

cos(x) -csc(x)

Explanation:

It is helpful to know the relations between the trig functions:

`\cot{x}=(cos(x))/(sin(x))\\\\\sec{x}=(1)/(cos(x))\\\\\csc{x}=(1)/(sin(x))`

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Then the given expression can be simplified as follows:

`\cot{x}(sin(x)-\sec{x})=(cos(x))/(sin(x))\left(sin(x)-(1)/(cos(x))\right)=cos(x)-(1)/(sin(x))\\\\=\boxed{cos(x)-\csc{x}}`