Question

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

Answer 1

Answer:

  cos(x) -csc(x)

Step-by-step explanation:

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

  $\cot{x}=\dfrac{\cos{x}}{\sin{x}}\\\\\sec{x}=\dfrac{1}{\cos{x}}\\\\\csc{x}=\dfrac{1}{\sin{x}}$

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Then the given expression can be simplified as follows:

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