Question

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

Answer 1

Answer:

cosA+sinA=2–√cosA

(2–√–1)cosA=sinA

cosA1=sinA2–√–1=cos2A+sin2A−−−−−−−−−−−−√1+(2–√–1)2−−−−−−−−−−√=14–22–√−−−−−−√=cosA−sinA1−(2–√–1)

So cosA−sinA=2−2–√4–22–√−−−−−−√=√2-√2÷2