Notes: `6cos^2(x) - 3` Use a double angle formula to rewrite the expression.

Sunday, 25 October 2015

By the double angle formula for cosine,

$\displaystyle{\cos{{\left({2}{x}\right)}}}={2}{{\cos}}^{{2}}{x}-{1}.$

Therefore our expression is equal to

$\displaystyle{6}{{\cos}}^{{2}}{\left({x}\right)}-{3}={3}{\left({2}{{\cos}}^{{2}}{\left({x}\right)}-{1}\right)}={3}{\cos{{\left({2}{x}\right)}}}.$

By the double angle formula for cosine,

$\displaystyle{\cos{{\left({2}{x}\right)}}}={2}{{\cos}}^{{2}}{x}-{1}.$

Therefore our expression is equal to

$\displaystyle{6}{{\cos}}^{{2}}{\left({x}\right)}-{3}={3}{\left({2}{{\cos}}^{{2}}{\left({x}\right)}-{1}\right)}={3}{\cos{{\left({2}{x}\right)}}}.$

Notes