If the middle term in the binomial expansion of 1 x + x s i n x 10 is 63 8 , then the value of 6 s i n 2 x + s i n x - 2 is

Question

If the middle term in the binomial expansion of 1 x + x s i n x 10 is 63 8 , then the value of 6 s i n 2 x + s i n x - 2 is,

MARKS App · Accepted Answer

Here, n = 10 , which is even. Middle term = 10 2 + 1 t h term = 6 t h term T 6 = 10 C 5 1 x 5 ( x sin x ) 5 ⇒ 63 8 = 252 s i n x 5 ⇒ s i n x 5 = 1 32 ⇒ s i n x 5 = 1 2 5 ⇒ s i n x = 1 2 ⇒ 2 s i n x - 1 = 0 ⇒ 6 s i n 2 x + s i n x - 2 = 2 s i n x - 1 3 s i n x + 2 = 0

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