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

Options

A. `sqrt(2)`
B. `1/sqrt(2)`
C. `1/2`
D. `0`

Answer

A

Explanation

Numerator `=2[(sin 1^(@)+sin89^(@))+(sin2^(@)+sin88^(@))+........+(sin 44^(@)+sin46^(@))+sin45^(@)]`
`rArr("Numerator")/("Denominator")`
`=2[sin 45^(@){cos44^(@)+cos43^(@)+.......+cos1^(@))+1}]`
`=2sin45^(@)=sqrt(2)`.