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

Problem

sin^2(x)*sec^2(x)−sin^2(x)

Solution

1. Factor out the common term sin^2(x) from the expression.

sin^2(x)*(sec^2(x)−1)

2. Identify the Pythagorean identity for secant and tangent, which states 1+tan^2(x)=sec^2(x)

tan^2(x)=sec^2(x)−1

3. Substitute the identity tan^2(x) into the expression.

sin^2(x)*tan^2(x)

Final Answer

sin^2(x)*sec^2(x)−sin^2(x)=sin^2(x)*tan^2(x)

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