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cosA+cos(12 0^(@)+A)+cos(12 0^(@)-A)=...

`cosA+cos(12 0^(@)+A)+cos(12 0^(@)-A)=`

Text Solution

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LHS`=cosA+cos(120^(@)+A)+cos(120^(@)-A)`
`=cosA+(cos120^(@)cosA-sin120^(@)sinA) + cos120^(@)cosA+sin120^(@)sinA`
`=cosA+2cos120^(@)cosA`
`=cosA+2cos(180^(@)-60^(@))cosA`
`cosA-2(1/2)cosA`
`=cosA-cosA=0=` RHS Hence proved
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