How to solve the problem??

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

1 Answer
Shwetank Mauria
Mar 23, 2018

Please see below.

Explanation:

#(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#

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