Simplify 1-2sin(22.5)^2

Problem

1−2*sin^2(22.5^∘)

Solution

1. Identify the expression as a specific form of a trigonometric identity.

2. Recall the double-angle formula for cosine, which states cos(2*θ)=1−2*sin^2(θ)

3. Substitute θ=22.5^∘ into the identity.

4. Calculate the resulting angle by multiplying 2×22.5^∘=45^∘

5. Evaluate the trigonometric value of cos(45^∘) using the unit circle.

Final Answer

1−2*sin^2(22.5^∘)=√(,2)/2

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