pls solve

Asked by pb_ckt | 14th Jun, 2019, 11:20: PM

Expert Answer:

begin mathsize 16px style We space have comma space cotA space plus cotB space plus space cotC space equals space 0
rightwards double arrow cosA over sinA plus cosB over sinB plus space cosC over sinC space equals space 0
rightwards double arrow cosB over sinB plus space cosC over sinC space equals space minus cosA over sinA
rightwards double arrow fraction numerator cosBsinC space plus cosCsinB space over denominator sinBsinC end fraction equals negative cosA over sinA
rightwards double arrow fraction numerator sin open parentheses straight B space plus space straight C close parentheses over denominator sinBsiC end fraction equals negative cosA over sinA
open parentheses ABC thin space is space straight a space traingle.
Sum space of space all space the space angles space of space straight a space triangle space is space 180 to the power of straight omicron equals space straight pi.
rightwards double arrow straight B thin space plus space straight C space equals space straight pi minus space straight A close parentheses
rightwards double arrow fraction numerator sin open parentheses straight pi minus straight A close parentheses over denominator sinBsiC end fraction equals negative cosA over sinA
rightwards double arrow sinA over sinBsiC equals negative cosA over sinA space
rightwards double arrow fraction numerator sin squared straight A over denominator sinBsiC end fraction space equals space minus cosA space space space.... space left parenthesis straight i right parenthesis
Similary comma space we space get
fraction numerator sin squared straight B over denominator sinAsiC end fraction space equals space minus cosB space space.... space left parenthesis ii right parenthesis
fraction numerator sin squared straight C over denominator sinAsinB end fraction space equals space minus cosC space space space.... space left parenthesis iii right parenthesis
Multiplying space equations space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get
rightwards double arrow space 1 space equals space minus cosAcosBcosC
rightwards double arrow cosAcosBcosC space equals space minus 1


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Answered by Yasmeen Khan | 15th Jun, 2019, 10:15: PM