so, \displaystyle { {\cos }^ {2}}x=\frac { {\left ( {\cos 2x~+1} \right)}} {2} cos2x = 2(cos2x + 1) . (iii) We will use this value of \displaystyle { {\cos }^ {2}}x cos2x and
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1) Recall the double angle formula: cos (2x) = cos^2 (x) - sin^2 (x). 2) We also know the trig identity sin^2 (x) + cos^2 (x) = 1, so combining these we get the equation cos (2x) = 2cos^2 (x)