Question

Simplify cot x – csc x cos x.1) cot x csc x – cot x cos x2) 03) 2 cot x4) 1

Answer 1

`2)0`

Step-by-step explanation

We want to simplify the trigonometric expression:

`\cot x-\csc x\cos x`

According to trigonometric ratios, we have that:

`\begin{gathered} \cdot\cot x=(1)/(\tan x)=(1)/((\sin x)/(\cos x))=(\cos x)/(\sin x) \\ \cdot\csc x=(1)/(\sin x) \end{gathered}`

Substitute those into the expression given:

`\begin{gathered} (\cos x)/(\sin x)-((1)/(\sin x))\cos x \\ \Rightarrow(\cos x)/(\sin x)-(\cos x)/(\sin x) \\ \Rightarrow0 \end{gathered}`

The answer is option 2.