Question

If cos+ sin = √2 cos show that cos-sin= √2 sin​

Answer 1

Step-by-step explanation:

cos-sin=√2sin

squad both sides

(cos-sin) ^2=(√2sin) ^2

cos^2+sin^2-2cossin=2sin^2

cos^2=2sin^2-sin^2+2cos sin

cos^2 =sin^2 + 2cos sin

adding cos both sides

cos^2+cos^2=sin^2+2cos sin + cos^2

2cos^2=(sin + cos) ^2

√(2cos^2)=sin + cos

√2 cos = cos + sin

hope it helps