Simplify 1/(cot(x)^2+1)

Problem

1/(cot2(x)+1)

Solution

1. Identify the trigonometric identity for the denominator. Recall the Pythagorean identity relating cotangent and cosecant.

cot2(x)+1=csc2(x)

2. Substitute the identity into the original expression to simplify the denominator.

1/csc2(x)

3. Apply the reciprocal identity for the cosecant function, where sin(x)=1/csc(x)

(1/csc(x))2=sin2(x)

Final Answer

1/(cot2(x)+1)=sin2(x)

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