Prove that: .

Formula : -

(i) Cos 3 a = 4 cos³ a – 3 cos a

(ii) sin3a = 3sina – 4sin³a

(iii) a³ – b³ = (a² – b²)(a² + b² + ab)

(iv) sin²a + cos²a = 1

Taking L.H.S we get,

using formula (i) and (ii)

taking common (cos a – sin a) and using formula (iii)

using formula(iv)

L.H.S = R.H.S

Hence, Proved.