Question

The series $f\left(x\right)=x+\frac{x^3}{3!}+\frac{x^5}{5!}+..$is the expansion of

• A. cosh x
• B. sin x
• C. sinh x
• D. cos x

Answer 1

The correct option is C sinh x

$sinhx=\frac{e^x-e^{-x}}{2}$
= $\frac{1}{2}[(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^3}{3!}+...)-(1-x+\frac{x^2}{2!}-\frac{x^3}{3!}...)]$
=$x+\frac{x^3}{3!}+\frac{x^5}{5!}+...$