Simplify sin(pi/9)^2+cos(pi/9)^2

Problem

sin2(π/9)+cos2(π/9)

Solution

1. Identify the structure of the expression as the sum of the squares of the sine and cosine of the same angle.

2. Recall the Pythagorean identity, which states that for any angle θ the sum of the squares of sine and cosine is always equal to 1

3. Apply the formula sin2(θ)+cos2(θ)=1 where θ=π/9

4. Conclude that since the identity holds for all real numbers, the value of the expression is 1

Final Answer

sin2(π/9)+cos2(π/9)=1

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