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Question
Prove the following:
`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`
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Solution
L.H.S. = `cos(pi/4 + x) + cos(pi/4 - x)`
= `2cos([pi/4 + x + pi/4 - x)/2)cos((pi/4 + x - (pi/4 - x))/2)`
= `2cos pi/4 cosx`
= `2(1/sqrt(2))cosx`
= `sqrt(2)cosx`
= R.H.S.
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