Let f n = sin ⁡ 1 × sin ⁡ 2 × . . . . . s i n n , ∀ n ∈ N , then the number of elements in the set A = f 1 , f 2 , . . . . . . . . . . , f 6 that are positive are

Step-by-step solution

sin ⁡ 1 ,   sin ⁡ 2 ,   sin ⁡ 3 are positive and sin ⁡ 4 ,   sin ⁡ 5 ,   sin ⁡ 6 are negative Hence f 1 ,   f 2 ,   f 3 ,   f 5 are positive while in f 4 there are exactly one negative and three positive terms. Similarly, f ( 6 ) is negative