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Prove that (i) "cos " ((pi)/(3) +x)...

Prove that
`(i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x)`
`(ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x`
`(iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) "`
`(iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0`

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