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    				| 1. | If `A+B+C=pi`, prove that : `cos2A+cos2B-cos2C=1-4sinA sinB cosC` | 
| Answer» We have `LHS=(cos2A+cos 2B)-cos 2C` `=2cos (A+B)cos (A-B)-2cos^(2)C+1` `=2cos (pi-C)cos (A-B)-2cos^(2)C+1` `=-2cos C cos (A-B)-2cos^(2)C+1` `=1-2 cos C [ cos (A-B)+cosC]` `=1-2cos C [cos(A-B)+cos{pi-(A+b)}]` `=1-2cos C [ cos (A-B)-cos (A+B)]` `=1-2 cos C [2sin A sin C=RHS.` `therefore cos 2A+cos2B-cos2C=1-4sin A sin B cos C.` | |