If I n = ∫ π 4 π 2 cot n x d x , then

Question

If I n = &#8747; &#960; 4 &#960; 2 cot n x d x , then

Aicharya · Accepted Answer

I n = &#8747; &#960; / 4 &#960; / 2 cot n x d x = &#8747; &#960; / 4 &#960; / 2 cot n - 2 x cosec 2 x - 1 d x = - cot n - 1 x n - 1 &#960; / 4 &#960; / 2 - I n - 2 = 1 n - 1 - I n - 2 &#8658; I n + I n - 2 = 1 n - 1 &#8658; I 2 + I 4 = 1 3 I 3 + I 5 = 1 4 I 4 + I 6 = 1 5 &#8756; 1 I 2 + I 4 , 1 I 3 + I 5 , 1 I 4 + I 6 are in A . P .

If I n = &#8747; &#960; 4 &#960; 2 cot n x d x , then

Solution

If I n = ∫ π 4 π 2 cot n x d x , then