Log of Sine

Algebra Level 4

If ${ e }^{ (\sin ^{ 2 }{ x } +\sin ^{ 4 }{ x } +\sin ^{ 6 }{ x } +..........\infty )\ln { 2 } }$ for $$0<x<\frac { \pi }{ 2 }$$ , satisfies the equation $${ x }^{ 2 }-9x+8=0$$ The value of $$\frac { 1 }{ 1 +\tan { x } }$$ is of the form $$\frac { \sqrt { a } -b }{ c }$$ . Find the value of $$\frac { a+b+c }{ 2 }$$

DETAILS

a is a square-free number and pairwise g.c.d. of a,b and c is 1

×