Simplify csc(( square root of 3)/2)

Problem

csc(√(,3)/2)

Solution

1. Identify the expression as the cosecant of a value given in radians, csc(x)

2. Apply the identity for cosecant, which is the reciprocal of the sine function.

csc(√(,3)/2)=1/sin(√(,3)/2)

3. Evaluate the expression numerically if needed, as √(,3)/2 is an angle in radians (approximately 0.866 rad) and not a standard angle whose sine is easily expressed in radicals.

4. Conclude that without further context for a decimal approximation, the simplest exact form is the reciprocal of the sine.

Final Answer

csc(√(,3)/2)=1/sin(√(,3)/2)

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