If A,BandC are interior angles of triangle ABC,then show thatSin(B+C b

1.	If A,BandC are interior angles of triangle ABC,then show thatSin(B+C by 2)=cosAby2
Answer» \xa0A, B, C, are interior angles of a\xa0{tex}\\Delta {/tex}{tex}\\because A + B + C = 180 ^ { 0 }{/tex}{tex}\\Rightarrow B + C = 180 ^ { 0 } - A \\Rightarrow \\frac { B + C } { 2 } = 90 ^ { 0 } - \\frac { A } { 2 }{/tex}{tex}\\Rightarrow \\sin \\frac { \\mathrm { B } + \\mathrm { C } } { 2 } = \\sin \\left( 90 ^ { \\circ } - \\frac { \\mathrm { A } } { 2 } \\right) \\left[ \\because \\sin \\left( 90 ^ { 0 } - \\theta \\right) = \\cos \\theta \\right]{/tex}{tex}\\Rightarrow \\sin \\frac { \\mathrm { B } + \\mathrm { C } } { 2 } = \\cos \\frac { \\mathrm { A } } { 2 } \\text { proved }{/tex}LHS = RHS

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