Simplify sin(x)^2+cos(x)^2+tan(x)^2

Problem

sin^2(x)+cos^2(x)+tan^2(x)

Solution

1. Identify the Pythagorean identity for sine and cosine, which states that sin^2(x)+cos^2(x)=1

2. Substitute the value 1 into the expression in place of sin^2(x)+cos^2(x)

1+tan^2(x)

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

Final Answer

sin^2(x)+cos^2(x)+tan^2(x)=sec^2(x)

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