If $\cos x=\frac{12}{13}$ and $\sin y=\frac{7}{25}$ then what is $\cos y$ and $\sin x$?

Question

Let $\cos x=\frac{12}{13}$ and $\sin y=\frac{7}{25}$.

Determine $\cos y$ and $\sin x$.

I know that there are basic ways of solving this, such as considering a right triangle, or using the Pythagorean theroem writing $\sin x =\sqrt{1-\cos^2x}$, but I was wondering if we could use another basic identity to solve the problem such as the sum or difference identity?

Thanks.

Answer 1

Hint. There are two moderately well known integer right triangles here, $$ (? , 12, 13) \text{ and } (7, ? , 25) \ . $$ You can find them with the Pythagorean theorem.

There is nothing "more basic" in trigonometry.