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We use the identities

Start with left hand side :

Start with left hand side :

### This Is a Certified Answer

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We know that standard identity:

here, A = 60-a and B = 60+a

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

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

= -1/4 * Cos (a) + 1/2 * 1/2 [ Cos 3a + cos a]

=

*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)*