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ICSE - X - Mathematics - Trigonometrical Identities

SinA - sinB/ cos A +Cos B   + cos A- cosB/sinA +sinB =0

Asked by adampur334 2nd October 2017, 4:19 PM
Answered by Expert

Answer:

begin mathsize 16px style fraction numerator Sin space straight A space minus space sin space straight B over denominator cosA space plus space cosB end fraction space plus space fraction numerator cosA space minus space cosB over denominator Sin space straight A space plus space sin space straight B end fraction
equals fraction numerator open parentheses Sin space straight A space minus space sin space straight B close parentheses begin display style open parentheses Sin space straight A space plus space sin space straight B close parentheses end style begin display style plus end style begin display style open parentheses cosA space minus space cosB close parentheses end style begin display style open parentheses cosA space plus space cosB close parentheses end style over denominator open parentheses cosA space plus space cosB close parentheses begin display style open parentheses Sin space straight A space plus space sin space straight B close parentheses end style end fraction
equals fraction numerator begin display style sin squared end style begin display style straight A end style begin display style space end style begin display style minus end style begin display style space end style begin display style begin display style sin end style squared end style begin display style space end style begin display style straight B end style begin display style space end style begin display style plus end style begin display style space end style begin display style begin display style cos end style squared end style begin display style space end style begin display style straight A end style begin display style space end style begin display style minus end style begin display style space end style begin display style begin display style cos end style squared end style begin display style space end style begin display style straight B end style over denominator open parentheses cosA space plus space cosB close parentheses open parentheses Sin space straight A space plus space sin space straight B close parentheses end fraction
equals fraction numerator sin squared straight A plus cos squared space straight A space minus open parentheses space sin squared space straight B plus cos squared space straight B close parentheses over denominator open parentheses cosA space plus space cosB close parentheses open parentheses Sin space straight A space plus space sin space straight B close parentheses end fraction
equals fraction numerator begin display style 1 space minus 1 end style over denominator begin display style open parentheses cosA space plus space cosB close parentheses open parentheses Sin space straight A space plus space sin space straight B close parentheses end style end fraction
equals 0
fraction numerator begin display style Sin space straight A space minus space sin space straight B end style over denominator begin display style cosA space plus space cosB end style end fraction space plus space fraction numerator begin display style cosA space minus space cosB end style over denominator begin display style Sin space straight A space plus space sin space straight B end style end fraction space equals space 0 space Hence comma space proved.
end style
Answered by Expert 3rd October 2017, 9:25 AM

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