Simplify sin(x)sec(x)cot(x)

Problem

sin(x)*sec(x)*cot(x)

Solution

1. Rewrite the trigonometric functions sec(x) and cot(x) in terms of sin(x) and cos(x) using the reciprocal and quotient identities.

sec(x)=1/cos(x)

cot(x)=cos(x)/sin(x)

2. Substitute these expressions back into the original product.

sin(x)⋅1/cos(x)⋅cos(x)/sin(x)

3. Cancel the common factors in the numerator and the denominator.

(sin(x)⋅cos(x))/(cos(x)⋅sin(x))

4. Simplify the resulting fraction.

1

Final Answer

sin(x)*sec(x)*cot(x)=1

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