Use a double angle formula to find the exact value of the gi

Use a double angle formula to find the exact value of the given expression

2 cos ^2 7pi/12 -1 =

(simplify your answer. Type an exact answer using radicals as needed. Use integers or fractions for any numbers in the expression.)

Solution

2cos²x -1=cos(2x)

2cos²(7pi/12) -1

=cos(2*7pi/12)

=cos(7pi/6)

=-cos(pi/6)

=-(3)_/2

so 2cos²(7pi/12) -1=-(3)_/2