Question

If A + B + C =  then prove that cos 2A + cos 2B + cos 2C = 1 + 4 sinA sinB sinC​

Answer 1

Step-by-step explanation:

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 CRead more on Sarthaks.com - https://www.sarthaks.com/535190/if-a-b-c-3-2-prove-that-cos-2a-cos-2b-cos-2c-1-4-sina-sin-b-sin-c

Answer 2

Answer:

+ 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 CRead more on Sarthaks.com - https://www.sarthaks.com/535190/if-a-b-c-3-2-prove-that-cos-2a-cos-2b-cos-2c-1-4-sina-sin-b-sin-c