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CBSE Class 11-science Answered

if cosA+sinA= underroot2 .cosA  then prove that   cosA-sinA= underroot2 . sinA
Asked by dalbirgolagarh | 19 Jul, 2016, 05:45: AM
answered-by-expert Expert Answer
begin mathsize 12px style cosA space plus space sinA space equals space square root of 2 space cosA Squaring space both space sides comma space we space get open parentheses cosA space plus space sinA space close parentheses squared equals space 2 space cos squared straight A rightwards double arrow cos squared straight A plus sin squared straight A space plus space 2 cosAsinA space equals space 2 space cos squared straight A rightwards double arrow cos squared straight A minus sin squared straight A space equals space 2 cosAsinA space rightwards double arrow left parenthesis cosA plus sinA right parenthesis left parenthesis cosA minus sinA right parenthesis equals space 2 cosAsinA space Substituting space left parenthesis cosA plus sinA right parenthesis equals square root of 2 space cosA comma space we space get square root of 2 space cosA left parenthesis cosA minus sinA right parenthesis equals space 2 cosAsinA space rightwards double arrow cosA minus sinA equals fraction numerator space 2 cosAsinA space over denominator square root of 2 space cosA end fraction equals square root of 2 sinA Hence comma space cosA minus sinA equals square root of 2 sinA end style
Answered by Rebecca Fernandes | 19 Jul, 2016, 08:48: AM

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