Simplify tan(x)^2-sec(x)^2

Problem

tan2(x)−sec2(x)

Solution

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

tan2(x)+1=sec2(x)

2. Rearrange the identity to isolate the terms present in the original expression by subtracting sec2(x) from both sides.

tan2(x)−sec2(x)+1=0

3. Subtract 1 from both sides to find the value of the expression.

tan2(x)−sec2(x)=−1

Final Answer

tan2(x)−sec2(x)=−1

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