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The sum of solutions of sin pi x+cos pi ...

The sum of solutions of `sin pi x+cos pi x=0` in `[0, 100]` is

A

4375

B

4975

C

5000

D

5025

Text Solution

Verified by Experts

The correct Answer is:
D
`sin pi x + cos pi x =0`
or `sin((pi)/(4)+pi x)=0`
or `(pi)/(4)+pi x = n pi, n in Z`
or `x = n -(1)/(4)` where `n in Z`
`Sum = sum_(n=1)^(100)(n-(1)/(4))`
`=(100xx101)/(2)-(100)/(4)`
`=5050-25`
`=5025`
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