Summing up factorials (3)

Calculus Level 5

\[ \sum_{ k=0 }^{ \infty }\sum_{ i=0 }^{ \infty } \dfrac{ { (-1) }^{ i+k } }{ \left( 2k+1 \right)!(2i)!(i+k+1) } = \sin^b(a) \] If the above equation is true for natural numbers \( a \) and \( b \). The find the value of \(a+b\).

Note: Angles are measured in radian.


Try part 1 and part 2 as well.
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