The value of expression `(2(sin1^0+sin2^0+sin3^0+...+sin89^0))/(2(cos1^0+cos2^0++cos44^0)+1)` (a)`sqrt(2)` (b) `1/(sqrt(2))` (c) `1/2` (d) 0

Explanation

`(2(sin1^@+sin2^@+sin3^@+...+sin89^@))/(2(cos1^@+cos2^@+cos3^@+...+cos44^@)+1)`

`=(2((sin1^@+sin89^@)+(sin2^@+sin88^@)+...+(sin44^@+sin46^@)+sin45^@))/(2(cos1^@+cos2^@+cos3^@+...+cos44^@)+1)`

`=(2(2sin45^@cos44^@)+(2sin45^@cos43^@)+...(2sin45^@cos1^@)+sin45^@)/(2(cos1^@+cos2^@+cos3^@+...+cos44^@)+1)`

`=(2*sin 45^@(2(cos1^@+cos2^@+cos3^@+...+cos44^@)+1))/(2(cos1^@+cos2^@+cos3^@+...+cos44^@)+1)`

`=2*sin45^@`

`=2(1/sqrt2)`

`=sqrt2`

so, option `(a)` is the correct option.