compute..

Question

Cos(1degree)+cos(3degree)+cos(5degree)+...+Cos(179degree)
plz show working even an hint can,t help me.Have been do maths alday my brain is fried..Ah thanks

Answer 1

cute problem

recall that cos x = - cos(180 - x)
that is
cos(1) = - cos(179)
cos(3) = - cos(177)
..
cos(89) = - cos(91)
cos(91) = - cos(89)
...
cos(177) = - cos(3)
cos(179) = - cos(1)

so :
cos1 + cos3 + ... + cos 177 + cos 179
= (cos1+cos179) + (cos3+cos177) + ...+ (cos89+cos91)
= 0+0+...+0+0

= 0