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Prove that: cos 55^0+cos 65^0+cos 175^0=...

Prove that: `cos 55^0+cos 65^0+cos 175^0=0`

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We have to proof,
`cos(55^o)+cos(65^o)+cos(175^o)=0`
Let,
L.H.S.=`cos(55^o)+cos(65^o)+cos(175^o)`
As we know the formula,
`cos(A^o)+cos(B^o)= 2[cos(((A^o) +(B^o))/2)cos(((A^o)-(B^o))/2)]`
then, L.H.S=`cos(55^o)+cos(65^o)+cos(175^0)`
L.H.S=`2[(cos(((55^o)+(65^o))/2)cos(((55^o)-(65^o))/2)]+cos(175^o)`
L.H.S=`2cos(60^o)cos(5^o) +cos(175^o)`
...
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