If ∫ 0 π / 3 tan ⁡ θ 2 k   sec ⁡ θ d θ = 1 - 1 2 ,   ( k > 0 ) , then the value of k is

Question

If &#8747; 0 &#960; / 3 tan &#8289; &#952; 2 k &#8201; sec &#8289; &#952; d &#952; = 1 - 1 2 , &#160; ( k &#62; 0 ) , then the value of k is

Aicharya · Accepted Answer

∫ 0 π / 3 tan ⁡ x 2 k sec ⁡ x d x = 1 2 k ∫ 0 π / 3 sin ⁡ x cos ⁡ x d x Put t = cos ⁡ x d t = - sin ⁡ x d x , also x = 0 , t = 1 ; x = π 3 , t = 1 2 ∴ 1 2 k ∫ 1 1 / 2 - d t t = 1 2 k ∫ 1 / 2 1 t - 1 2 d t = 1 2 k × 2 t 1 2 1 / 2 1 = 2 k 1 - 1 2 = 2 - 1 k Given 2 - 1 k = 1 - 1 2 = 2 - 1 2 ∴ k = 2

If ∫ 0 π / 3 tan ⁡ θ 2 k   sec ⁡ θ d θ = 1 - 1 2 ,   ( k…

Solution

If &#8747; 0 &#960; / 3 tan &#8289; &#952; 2 k &#8201; sec &#8289; &#952; d &#952; = 1 - 1 2 , &#160; ( k…

Solution

If ∫ 0 π / 3 tan ⁡ θ 2 k sec ⁡ θ d θ = 1 - 1 2 , ( k…