Answer the following questions related to the expression cos2θ.
a. (i) Starting only with the identity sin2θ+cos2θ=1, obtain three algebraically equivalent expressions for cos2θ.
b. (ii) Show algebraically that the expressions obtained in part (i) are indeed equal by transforming any two of them into the third form.
c. (iii) Taking θ=30∘, calculate the numerical value of cos2θ using each of the three forms and verify that the answers agree.