In a right triangle abc,right -angled at B, if tan A= 1 ,then verify that2 sin A cos A =1.

In a right triangle abc,right -angled at B, if tan A= 1 ,then verify t

1.	In a right triangle abc,right -angled at B, if tan A= 1 ,then verify that2 sin A cos A =1.
Answer» In {tex} \\triangle A B C{/tex},{tex}\\tan A = 1{/tex}{tex}\\Rightarrow \\quad \\frac { B C } { A C } = 1{/tex}{tex}\\Rightarrow {/tex}\xa0BC = x and\xa0AC = xUsing Pythagoras theorem,\xa0{tex}\\Rightarrow A B ^ { 2 } = A C ^ { 2 } + B C ^ { 2 }{/tex}{tex}\\Rightarrow \\quad A B ^ { 2 } = x ^ { 2 } + x ^ { 2 }{/tex}{tex}\\Rightarrow \\quad A B = \\sqrt { 2 } x{/tex}{tex}\\therefore \\quad \\sin A = \\frac { B C } { A B } = \\frac { x } { \\sqrt { 2 } x } = \\frac { 1 } { \\sqrt { 2 } } \\text { and } \\cos A = \\frac { A C } { \\sqrt { 2 } x } = \\frac { x } { \\sqrt { 2 } x } = \\frac { 1 } { \\sqrt { 2 } } {/tex}2 sin A cos A\xa0{tex}= 2 \\times \\frac { 1 } { \\sqrt { 2 } } \\times \\frac { 1 } { \\sqrt { 2 } } = 1{/tex}