Simplify 1-2sin((7pi)/12)^2

Problem

1−2*sin2((7*π)/12)

Solution

1. Identify the trigonometric identity for the double angle of cosine. The identity is given by cos(2*θ)=1−2*sin2(θ)

2. Substitute the value θ=(7*π)/12 into the identity.

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

cos(2⋅(7*π)/12)=cos((7*π)/6)

4. Evaluate the cosine of the resulting angle. The angle (7*π)/6 is in the third quadrant where cosine is negative, and its reference angle is π/6

cos((7*π)/6)=−√(,3)/2

Final Answer

1−2*sin2((7*π)/12)=−√(,3)/2

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