Simplify 2cos((5pi)/8)^2-1

Problem

2*cos2((5*π)/8)−1

Solution

1. Identify the double-angle identity for cosine, which states cos(2*θ)=2*cos2(θ)−1

2. Substitute the value θ=(5*π)/8 into the identity.

3. Multiply the angle by 2 to find the equivalent cosine expression.

2*((5*π)/8)=(5*π)/4

4. Evaluate the cosine of the resulting angle using the unit circle.

cos((5*π)/4)=−√(,2)/2

Final Answer

2*cos2((5*π)/8)−1=−√(,2)/2

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