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    				| 1. | If `A+B+C=pi`, prove that : `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2 =1` | 
| Answer» Here , `A+B+C=pi` `implies((A)/(2)+(B)/(2))=((pi)/(2)-( C)/(2))` `implies tan ((A)/(2)+(B)/(2))=tan ((pi)/(2)-( C)/(2))=cot ""(C)/(2)` `implies (tan ""(A)/(2)+tan ""(B)/(2))/(1-tan""(A)/(2)tan""(B)/(2))=(1)/(tan""( C)/(2))` `implies tan ""(C)/(2)tan ""(A)/(2)+tan ""(B)/(2)tan ""( C)/(2)=1-tan""(A)/(2) tan""(B)/(2)` `implies tan""(A)/(2)tan ""(B)/(2)+tan ""(B)/(2)tan ""( C)/(2)+tan""(C )/(2)tan""(A)/(2)+1.` | |