If cosA+sinA=√2,prove that cosA-sinA=√2sinA

Asked by ihsanansar123 | 20th Feb, 2018, 11:58: AM

Expert Answer:

begin mathsize 16px style cos space straight A plus sin space straight A equals square root of 2 cos space straight A
rightwards double arrow left parenthesis cos space straight A plus sin space straight A right parenthesis squared equals 2 cos squared space straight A
rightwards double arrow cos squared space straight A plus sin squared space straight A plus 2 cos space straight A space sin space straight A equals 2 space cos squared space straight A
rightwards double arrow cos squared space straight A minus 2 cos space straight A space sin space straight A equals sin squared space straight A
rightwards double arrow cos squared space straight A minus 2 cos space straight A space sin space straight A plus sin squared space straight A equals 2 sin squared space straight A
rightwards double arrow left parenthesis cos space straight A minus sin space straight A right parenthesis squared equals 2 space sin squared space straight A
rightwards double arrow cos space straight A minus sin space straight A equals square root of 2 space sin space straight A
end style

Answered by Rashmi Khot | 20th Feb, 2018, 12:39: PM