Simplify square root of (cos(x))/(tan(x))

Problem

√(,cos(x)/tan(x))

Solution

1. Express the tangent function in terms of sine and cosine using the identity tan(x)=sin(x)/cos(x)

√(,cos(x)/sin(x)/cos(x))

2. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

√(,cos(x)⋅cos(x)/sin(x))

3. Multiply the terms in the numerator.

√(,cos2(x)/sin(x))

4. Apply the property of radicals √(,a/b)=√(,a)/√(,b) to separate the numerator and denominator.

√(,cos2(x))/√(,sin(x))

5. Simplify the square root of the squared term, assuming the expression is defined in a domain where cos(x)≥0

cos(x)/√(,sin(x))

Final Answer

√(,cos(x)/tan(x))=cos(x)/√(,sin(x))

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