Question

If cos θ − sin θ = √2 sin θ, prove that cos θ + sin θ = √2 cos θ

Answer 1

Do you know the identity that \[\cos ^{2}\theta + \sin ^{2}\theta =1\]

Answer 2

I am sorry you won't even need to know the above

Answer 3

Square both sides:
you will get :\[\cos^2 \theta -2 \cos \theta \sin \theta + \sin^2 \theta = 2 \sin^2 \theta\]

Answer 4

Now you can arrange the expression to write \[\cos^2 \theta - \sin^2 \theta = 2\cos \theta \sin \theta\]

Answer 5

you can see on the left side - it is of the form a^2 -b^2 = (a-b)(a+b)
You know (a-b). So I guess you can do it from here