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

Problem

sin2(x)+cos2(x)+tan2(x)

Solution

1. Identify the Pythagorean identity for sine and cosine, which states that sin2(x)+cos2(x)=1

2. Substitute the value 1 into the expression in place of sin2(x)+cos2(x)

1+tan2(x)

3. Apply the Pythagorean identity for tangent and secant, which states that 1+tan2(x)=sec2(x)

Final Answer

sin2(x)+cos2(x)+tan2(x)=sec2(x)

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