Simplify 1/(sec(x)^2)

Problem

1/sec2(x)

Solution

1. Identify the reciprocal identity for the secant function.

2. Recall that the secant function is defined as the reciprocal of the cosine function.

sec(x)=1/cos(x)

3. Apply the identity to the squared term in the denominator.

sec2(x)=1/cos2(x)

4. Substitute this into the original expression and simplify the fraction.

1/1/cos2(x)=cos2(x)

Final Answer

1/sec2(x)=cos2(x)

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