If A + B + C = (3π/2) prove that Cos 2A + Cos 2B + Cos 2C = 1 – 4 S

1.	If A + B + C = (3π/2) prove that Cos 2A + Cos 2B + Cos 2C = 1 – 4 SinA.Sin B.Sin C.
Answer» A + B + C = 3π/2 ---------(1) L.H.S = cos 2A + cos 2B + cos 2C = 2 cos (A + B). cos (A – B) + 1 – 2 sin² C = 2 cos (270° – C). cos (A – B) – 2 sin² C = 1 – 2 sin C [cos (A – B) –2 sin² C = 1 – 2 sin C[cos (A – B) + sin C] = 1 – 2 sin C [cos (A – B) + sin (270° - bar(A + B))] = 1 – 2 sin C [cos (A – B) – cos (A + B)] = 1 – 2 sin C [2 sin A sin B] = 1 – 4 sin A sin B sin C

If A + B + C = (3π/2) prove that Cos 2A + Cos 2B + Cos 2C = 1 – 4 SinA.Sin B.Sin C.

Answer»

A + B + C = 3π/2 ---------(1)

L.H.S = cos 2A + cos 2B + cos 2C

= 2 cos (A + B). cos (A – B) + 1 – 2 sin² C

= 2 cos (270° – C). cos (A – B) – 2 sin² C

= 1 – 2 sin C [cos (A – B) –2 sin² C

= 1 – 2 sin C[cos (A – B) + sin C]

= 1 – 2 sin C [cos (A – B) + sin (270° - bar(A + B))]

= 1 – 2 sin C [cos (A – B) – cos (A + B)]

= 1 – 2 sin C [2 sin A sin B]

= 1 – 4 sin A sin B sin C

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If A + B + C = (3π/2) prove that Cos 2A + Cos 2B + Cos 2C = 1 – 4 SinA.Sin B.Sin C.

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