Question 1151362

{{{cos(3x)=cos^3(x)-3sin^2(x)cos(x)}}}


use identity: {{{cos(alpha + beta) = cos(alpha) cos(beta)- sin(alpha) sin(beta)}}}


write {{{cos(3x)}}} as {{{cos(2x+x)}}} which is equal to {{{cos(2x) cos(x) - sin(2x) sin(x)}}}


{{{cos(3x)=cos(2x) cos(x) - sin(2x) sin(x)}}}..........since {{{cos(2x)=cos(x+x)=cos(x) cos(x) - sin(x) sin(x)}}} and {{{sin(2x)=2 sin(x) cos(x)}}} we have

{{{cos(3x)=(cos(x) cos(x) - sin(x) sin(x)) cos(x) -(2 sin(x) cos(x)) sin(x)}}}


{{{cos(3x)=(cos^2(x)  - sin^2(x) ) cos(x) -2 sin^2(x) cos(x))}}}


{{{cos(3x)=cos^3(x)  - sin^2(x) cos(x) -2 sin^2(x) cos(x))}}}


{{{cos(3x)=cos^3(x)  - 3sin^2(x)* cos(x) }}}