If the greatest value of the term independent of x in the expansion of x sin α + a cos α x 10 is 10 ! 5 ! 2 , then the value of a is equal to:

Step-by-step solution

We have, r th term in the expansion of x sin α + a cos α x 10 is T r + 1 = C r 10 x sin α 10 - r a cos α x r r = 0 , 1 , 2 , … , 10 T r + 1 will be independent of x , when 10 - 2 r = 0 ⇒ r = 5 Now, T 6 = C 5 10 x sin α 5 × a cos α x 5 = C 5 10 × a 5 × 1 2 5 sin 2 α 5 T 6 will be greatest, when sin 2 α = 1 Therefore, C 5 10 a 5 2 5 = C 5 10 ⇒ a = 2