If cos π 4 cos π 8 cos π 16 cos π 32 = 2 m cosec π n then m + n =

Step-by-step solution

cos π 4 cos π 8 cos π 16 cos π 32 = 2 m cosec π n L H S = 1 2 sin π 2 n 2 cos π 2 n sin π 2 n cos π 2 n - 1 . . . . . . . . . . cos π 4 1 2 cos π 2 n 2 sin π 2 n - 1 cos π 2 n - 1 cos π 2 n - 2 . . . . . . . . . . cos π 4 1 2 × 2 2 cos e c π 2 n 2 sin π 2 n - 2 cos π 2 n - 2 cos π 2 n - 2 . . . . . . . . . . cos π 4 1 2 n - 2 cos e c π 2 n 2 sin π 8 cos π 8 cos π 4 1 2 × 2 n - 2 cos e c