Saved Bookmarks
| 1. |
If A,B and C are the interior angles of triangle ABC, find that tan(B+C)/2 |
| Answer» In\xa0{tex} \\Delta A B C{/tex}, we have,A + B + C = 180°{tex} \\Rightarrow{/tex}\xa0B + C =180° - ADividing 2 on both sides, we get\xa0{tex} \\Rightarrow \\quad \\frac { B + C } { 2 } = 90 ^ { \\circ } - \\frac { A } { 2 }{/tex}Applying Tan on both sides\xa0{tex} \\Rightarrow \\tan \\left( \\frac { B + C } { 2 } \\right){/tex}{tex} = \\tan \\left( 90 ^ { \\circ } - \\frac { A } { 2 } \\right){/tex}{tex} \\Rightarrow \\tan \\left( \\frac { B + C } { 2 } \\right) = \\cot \\frac { A } { 2 }{/tex} | |