Question number 33 and 32 (hand written only) 

32.Prove that, cos 6$\theta$ = 32 cos⁶ $\theta$ $-$ 48 cos⁴ $\theta$ + 18 cos⁴ $\theta$ $-$1

33. Prove that
           cos 4$\theta$ $-$ cos4a = 8 (cos$\theta$ $-$cos $\alpha$ ) (cos$\theta$ $-$cos $\alpha$ ) (cos$\theta$ $-$sin $\alpha$ ) (cos$\theta$+sin $\alpha$ )