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Question

$If,cscA+cscB+cscC=0$ ,then show that $(sumsinA)^2=sumsin^2A$

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Answer 1 · 2018-03-23T07:46:38

Please see below.

$(sumsinA)^2=(sinA+sinB+sinC)^2$

= $sin^2A+sin^2B+sin^2C+2sinAsinB+2sinBsinC+2sinCsinA$

= $sumsin^2A+2sinAsinB+2sinBsinC+2sinCsinA$

= $sumsin^2A+2sinAsinBsinC(1/sinC+1/sinB+1/sinA)$

= $sumsin^2A+2sinAsinBsinC(cscC+cscB+cscA)$

= $sumsin^2A+2sinAsinBsinCxx0$

= $sumsin^2A$