Problem

The key is to recognize that $\sin x$ and $\cos x$ are linked by the Pythagorean identity, so you can't solve them independently. Square both sides to eliminate the sum, which will give you a relationship involving $\sin x \cos x$—then use that identity to find what values actually work. Just remember that squaring can introduce extraneous solutions, so you'll need to check your answers in the original equation.

The key is to recognize that $\sin x$ and $\cos x$ are linked by the Pythagorean identity, so you can't solve them independently. Square both sides to eliminate the sum, which will give you a relationship involving $\sin x \cos x$—then use that identity to find what values actually work. Just remember that squaring can introduce extraneous solutions, so you'll need to check your answers in the original equation.