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

Problem

1/(tan2(x)+1)

Solution

1. Identify the trigonometric identity for the denominator.

2. Apply the identity tan2(x)+1=sec2(x) to rewrite the expression.

1/(tan2(x)+1)=1/sec2(x)

3. Use the reciprocal identity 1/sec(x)=cos(x) to simplify the fraction.

1/sec2(x)=cos2(x)

Final Answer

1/(tan2(x)+1)=cos2(x)

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