Answer:
The arranged steps are shown below.
Step-by-step explanation:
The given expression is
[tex]\cos 3x[/tex]
We need to express the given expression in terms of cos x.
The arranged steps are shown below:
[tex]\cos (2x+x)[/tex]
[tex]\cos (2x)\cos (x)-\sin (2x)\sin (x)[/tex]
[tex][1-2\sin^2 (x)]\cos (x)-[2\sin (x)\cos (x)]\sin (x)[/tex] [tex][\because \cos (2x)=1-2\sin^2 (x),\sin (2x)=2\sin (x)\cos (x)][/tex]
[tex]\cos (x)-2\sin^2 (x)\cos (x)-2\sin^2 (x)\cos (x)[/tex]
[tex]\cos (x)-4\sin^2 (x)\cos (x)[/tex]
[tex]\cos (x)[1-4\sin^2 (x)][/tex]
[tex]\cos (x)\{1-4[1-\cos^2 (x)]\}[/tex] [tex][\because \sin^2 (x)=1-\cos^2 (x)][/tex]
[tex]\cos (x)[-3+4\cos^2 (x)][/tex]
[tex]4\cos^3 (x)-3\cos (x)[/tex]
