Simplify 1-sec(x)^2

Problem

1−sec2(x)

Solution

1. Identify the fundamental Pythagorean identity relating the secant and tangent functions.

1+tan2(x)=sec2(x)

2. Rearrange the identity to isolate the expression that matches the given problem by subtracting sec2(x) and tan2(x) from both sides.

1−sec2(x)=−tan2(x)

3. Substitute the result of the identity into the original expression.

1−sec2(x)=−tan2(x)

Final Answer

1−sec2(x)=−tan2(x)

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