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Prove that: cos 100^0+cos 20^0=cos 40^0...

Prove that: `cos 100^0+cos 20^0=cos 40^0`

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We have to proof,
`cos(100^o)+cos(20^o)=cos(40^o)`
Let,
L.H.S.=`cos(100^o)+cos(20^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(100^o)+cos(20^o)`
L.H.S=`2cos(60^o)cos(40^o)`
L.H.S=`2*1/2cos(40^o)`
...
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