Mathematics

Problem

Consider the expression

P(x)=1-2\sin^{2}\left(\dfrac{3x}{2}-\dfrac{\pi}{4}\right)

. a. (i) Rewrite

P(x)

in the simplest form involving the cosine of a single angle without squared terms. b. (ii) Using the simplified form, evaluate

P(x)

when

x=60^{\circ}

. c. (iii) Find the range of

P(x)

for all real

x