## Answer :

[tex]\cos(x-y)\cos(x+y)=\cos^2y-\sin^2x[/tex]

[tex]\cos(3x)=4\cos^3(x)-3\cos(x)[/tex]

Start with left hand side :

[tex]\cos(a)\cos(60-a)\cos(60+a)\\=\cos(a)\left(\cos^2(a)-\sin^2(60)\right)\\=\cos(a)\left(\cos^2(a)-\frac{3}{4}\right)\\=\dfrac{4\cos^3(a)-3\cos(a)}{4}\\=\dfrac{\cos(3a)}{4}[/tex]

*2 Cos A Cos B = Cos (A+B) + Cos (A-B)*here, A = 60-a and B = 60+a

*Cos (a) Cos (60 - a ) Cos (60+a)**= Cos (a) * 1/2 * [ Cos (60-a+60+a) + Cos (60-a- 60-a) ]*

*= Cos (a) * 1/2 * [ Cos 120 + Cos (-2a) ]*

= 1/2 * Cos (a) * [ -1/2 + Cos (2a) ]

= -1/4 * Cos (a) + 1/2 Cos (a) Cos (2a) ---

**apply the above identity again**= -1/4 * Cos (a) + 1/2 * 1/2 [ Cos 3a + cos a]

=

*1/4 * Cos (3a)*