Simplify cos(15)^2-sin(15)^2

Problem

cos2(15)−sin2(15)

Solution

1. Identify the trigonometric identity for the double angle of cosine.

cos(2*θ)=cos2(θ)−sin2(θ)

2. Substitute the value θ=15 into the identity.

cos2(15)−sin2(15)=cos(2⋅15)

3. Multiply the values inside the cosine function.

cos(2⋅15)=cos(30)

4. Evaluate the cosine of 30 using the unit circle or standard trigonometric values.

cos(30)=√(,3)/2

Final Answer

cos2(15)−sin2(15)=√(,3)/2

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