Question

find value of cos 1+cos2+.....+cos 179

Answer 1

S=cos1+cos2+.......+cos179

and now you have to write this sum in reverse way :

like that:

S=cos179+cos178+........................+cos1

S=cos1    +cos2   +.........................+cos179( you have to gather)

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2S=(cos179+cos1)+(cos178+cos2)+................+(cos1+cos179)

and now you can see that:

cos 179+cos1=2x((cos179+1):2) x(cos(179-1):2)=0

cos 178+cos2=0

2S=0   S=0