(a) Using the exact values of the sine and cosine of 1/6π and 3/4π, and one of
the sum and difference formulas, show that the exact value of cos(7/12π) is 1/4(√2 − √6)
(b) (i) Using an appropriate double-angle formula, express sin(4θ) in
terms of sin(2θ) and cos(2θ).
(ii) Using your answer to part(b)(i) and appropriate double-angle
formulas, derive the formula
sin(4θ) = 4 sin θ cos3 θ − 4 sin3 θ cos θ.
(c) Given that cosec θ = −2, tan θ = 1/3 √3 and −π < θ < π, find the exact
value of the angle θ in radians. Justify your answer.
(d) Given that −1/2π < θ < 0 and sin θ = −3/4, use appropriate
trigonometric formulas to find the exact values of the following.
(ii) cos θ