If the middle term of 1x+xsinx10 is equal to 778 , then the value of x is
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a
2nπ+π6,n∈z
b
nπ+π6,n∈z
c
nπ+−1nπ6,n∈z
d
nπ+−1nπ3,n∈z
answer is C.
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Detailed Solution
1x+xsinx10 n=10 is even M. T=T102+1=T5+1=778⇒10c51x5(xsinx)5=638⇒10×9×8×7×65×4×3×2×11x5x5sin5x=638⇒63×4sin5x=638⇒sin5x=132⇒sinx=12⇒x=nπ+(−1)nπ6,n∈z