Simplify the trigonometric expression.
\[
\frac{\csc (x)-\sin (x)}{\cot (x)}
\]

Answer

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Final Answer: The simplified form of the given trigonometric expression is \(\boxed{\cos(x)}\)

Steps

Step 1 ：Given the trigonometric expression \(\frac{\csc (x)-\sin (x)}{\cot (x)}\)

Step 2 ：Convert all trigonometric functions to their basic forms. The basic forms of trigonometric functions are sine, cosine and tangent. Here, cosec(x) is the reciprocal of sin(x) and cot(x) is the reciprocal of tan(x).

Step 3 ：So, we can rewrite the expression in terms of sin(x) and tan(x) as \((-\sin(x) + \frac{1}{\sin(x)})\cdot \tan(x)\)

Step 4 ：Simplify the expression to get \(\cos(x)\)

Step 5 ：Final Answer: The simplified form of the given trigonometric expression is \(\boxed{\cos(x)}\)

Simplify the trigonometric expression.\[\frac{\csc (x)-\sin (x)}{\cot (x)}\]

Answer

Popular Problems

Simplify the trigonometric expression.
\[
\frac{\csc (x)-\sin (x)}{\cot (x)}
\]