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The value of the expression (2(sin1^@+si...

The value of the expression `(2(sin1^@+sin2^@+sin3^@+....+sin89^@))/(2(cos1^@+cos2^@+....+cos44^@)+1)` equals

A

`sqrt(2)`

B

`1/sqrt(2)`

C

`1/2`

D

`0`

Text Solution

Verified by Experts

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