Question: If the system of equations $\sin x \cos 2y = (a^2 - 1)^2 + 1$ and $\cos x \sin 2y = (a+1)$ has a sol...

Question

If the system of equations $\sin x \cos 2y = (a^2 - 1)^2 + 1$ and $\cos x \sin 2y = (a+1)$ has a solution, then the value of a+2 is ____.

Answer 1

Solution

To ensure the RHS of (1) is within the range $[-1,1]$ , we must have $(a^2-1)^2=0$ so that $a=\pm1$ . Testing in (2) shows $a=1$ gives an impossible value, so $a=-1$ is valid. Hence, $a+2=1$ .