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CBSE Class 12-science Answered

$I f space a comma b comma c space a r e space s u c h space t h a t space a plus b plus c equals 0 space t h e n space p r o v e space open vertical bar table row 1 cell cos c end cell cell cos b end cell row cell cos c end cell 1 cell cos a end cell row cell cos b end cell cell cos a end cell 1 end table close vertical bar$ =0

Asked by Eng.surinder.singh | 27 Jan, 2019, 07:49: PM

Expert Answer

Given determinant is expanded as

begin mathsize 12px style D space equals space 1 open parentheses 1 minus cos squared a close parentheses space minus space cos c space open parentheses cos c space minus cos a space cos b close parentheses plus cos b open parentheses cos c space cos a space minus space cos b close parentheses D space equals space 1 minus cos squared a space minus cos squared b minus cos squared c plus 2 cos a space cos b space cos c i f left parenthesis a plus b plus c right parenthesis equals 0 comma space t h e n space cos c space equals cos left square bracket negative left parenthesis a plus b right parenthesis right square bracket space equals space cos left parenthesis a plus b right parenthesis h e n c e space D space equals space 1 minus cos squared a space minus cos squared b minus cos squared left parenthesis a plus b right parenthesis plus 2 cos a space cos b space cos left parenthesis a plus b right parenthesis D space equals space 1 minus cos squared a minus cos squared b space minus cos squared a space cos squared b space minus space sin squared a sin squared b minus 2 cos a space cos b space sin a space sin b space plus 2 cos squared a space cos squared b space plus space 2 space cos a space cos b space sin a space sin b D space equals space 1 minus cos squared a minus cos squared b space minus cos squared a space cos squared b space minus space open parentheses 1 minus cos squared a close parentheses open parentheses 1 minus cos squared b close parentheses space plus space 2 cos squared a space cos squared b space I t space c a n space b e space p r o v e d comma space R H S space o f space t h e space a b o v e space e x p r e s s i o n space b e c o m e s space z e r o end style

Answered by Thiyagarajan K | 28 Jan, 2019, 11:08: AM

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