Complete the following and show all work.

a. Use a half-angle formula to find the exact value of the sin 67.5.

b. Use the half-angle formulas to find the exact value of cos 7pi/12

c. Use the half-angle formulas to find the exact value of the tan (pi/8)

d. Find the exact solutions in the interval [0,2] forx/2 = sin (x/2)

e. Rewrite the following expression in terms of the first power of cosine.

tan²x sin²x