Simplify 1/(cos(x)^2)

Problem

1/cos^2(x)

Solution

1. Identify the trigonometric reciprocal identity for the cosine function.

2. Recall that the secant function is defined as the reciprocal of the cosine function, expressed as sec(x)=1/cos(x)

3. Apply the power rule for identities, which states that 1/cos^n(x)=sec^n(x)

4. Substitute the identity into the expression to simplify 1/cos^2(x) to sec^2(x)

Final Answer

1/cos^2(x)=sec^2(x)

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