Simplify cos(pi/7)

Problem

cos(π/7)

Solution

1. Identify the expression as the cosine of a specific angle, π/7 radians.

2. Determine if the angle is a standard value on the unit circle. The angle π/7 (approximately 25.71 is not one of the common angles like 0 π/6 π/4 π/3 or π/2

3. Evaluate for exact algebraic forms. While cos(π/7) can be expressed as a root of a cubic equation 8*x3−4*x2−4*x+1=0 it does not simplify into a standard radical form involving only square roots.

4. Conclude that the expression is already in its simplest exact trigonometric form.

Final Answer

cos(π/7)=cos(π/7)

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