If tan=1/3 and tan b=1/2 . prove that sin2(a+b)=1

1.	If tan=1/3 and tan b=1/2 . prove that sin2(a+b)=1
Answer» {tex}Given\\,that{/tex}{tex}\\tan A = {1 \\over 3}\\,and\\,\\tan B = {1 \\over 2}{/tex}{tex}Now\\,\\,\\tan \\left( {A + B} \\right) = {{\\tan A + \\tan B} \\over {1 - tan A \\cdot \\tan B}}{/tex}{tex} = {{\\left( {{1 \\over 3} + {1 \\over 2}} \\right)} \\over {\\left( {1 - {1 \\over 3} \\cdot {1 \\over 2}} \\right)}}{/tex}{tex} = {{\\left( {{5 \\over 6}} \\right)} \\over {\\left( {{5 \\over 6}} \\right)}}{/tex}{tex}\\tan \\left( {A + B} \\right) = 1{/tex}{tex}A + B = {45^ \\circ }{/tex}{tex}Now\\,Sin2\\left( {A + B} \\right) = \\sin \\left( {2 \\times {{45}^ \\circ }} \\right){/tex}{tex} = \\sin {90^ \\circ }{/tex}{tex}\\sin 2\\left( {A + B} \\right) = 1{/tex}

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