If the middle term in the expansion of 1 x + x sin x 10 is equal to 7 7 8 , then the number of values of x in 0 , 2 π is equal to

Step-by-step solution

There are 11 terms in the expansion ⇒ 6 t h term is the middle term T 6 = C 5 10 1 x 5 x sin ⁡ x 5 ⇒ C 5 10 sin ⁡ x 5 = 63 8 ⇒ 10 × 9 × 8 × 7 × 6 5 × 4 × 3 × 2 sin ⁡ x 5 = 63 8 ⇒ sin ⁡ x 5 = 63 8 × 5 × 4 × 3 × 2 10 × 9 × 8 × 7 × 6 ⇒ sin ⁡ x = 1 2 Hence, there are 2 values of x in 0 , 2 π