I'm asked to prove something:

If $\sin\theta + \cos\theta = \sqrt{2}\sin\theta$ then show that $\cos\theta - \sin\theta = \sqrt{2}\cos\theta$.

I don't even think that's correct, because multiplying both equations, I get $\cos^2\theta - \sin^2\theta = 2\sin\theta\cos\theta \Rightarrow \cos(2\theta) = \sin(2\theta)$. That's wrong. Totally wrong.

Question

I'm asked to prove something:

If $\sin\theta + \cos\theta = \sqrt{2}\sin\theta$ then show that $\cos\theta - \sin\theta = \sqrt{2}\cos\theta$.

I don't even think that's correct, because multiplying both equations, I get $\cos^2\theta - \sin^2\theta = 2\sin\theta\cos\theta \Rightarrow \cos(2\theta) = \sin(2\theta)$. That's wrong. Totally wrong.

parthkohli · Answer

But there are cases where $\cos(2\theta) = \sin(2\theta)$. Well...

parthkohli · Answer

@ajprincess Please help :P

parthkohli · Answer

I'm thinking of squaring both the sides.

whpalmer4 · Answer

None of the first 4 solutions where $\cos(2\theta) = \sin(2\theta)$ appear to satisfy the equation you are asked to prove...

parthkohli · Answer

Yay, thanks! :-)