Trigonometry Series(Taylor Series)

Calculus Level 3

\[ \large \frac { 1 }{ 1! } +\frac { 1 }{ 2! } -\frac { 1 }{ 3! } -\frac { 1 }{ 4! } +\frac { 1 }{ 5! } +\frac { 1 }{ 6! } -\frac { 1 }{ 7! } -\frac { 1 }{ 8! } +\cdots = \, ? \]

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