if cosA+sinA= underroot2 .cosA  then prove that   cosA-sinA= underroot2 . sinA

Asked by dalbirgolagarh | 19th Jul, 2016, 05:45: AM

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 | 19th Jul, 2016, 08:48: AM

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