Verify the Identity 2-sec(x)^2=1-tan(x)^2

Problem

2−sec2(x)=1−tan2(x)

Solution

1. Identify the Pythagorean identity that relates the secant and tangent functions.

tan2(x)+1=sec2(x)

2. Substitute the expression 1+tan2(x) for sec2(x) into the left side of the equation.

2−(1+tan2(x))

3. Distribute the negative sign through the parentheses.

2−1−tan2(x)

4. Simplify the expression by subtracting the constants.

1−tan2(x)

Final Answer

2−sec2(x)=1−tan2(x)

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