Given $\sin x=\dfrac35$ with $x$ obtuse and $\cos y=\dfrac{24}{25}$ with $y$ acute, the exact value of $\cos(x+y)$ is:

1. Since $x$ is obtuse, $\cos x$ is negative: $\cos x=-\dfrac45$. 2. Since $y$ is acute, $\sin y$ is positive: $\sin y=\dfrac{7}{25}$. 3. Use $\cos(x+y)=\cos x\cos y-\sin x\sin y$. 4. $=\left(-\dfrac45\right)\left(\dfrac{24}{25}\right)-\left(\dfrac35\right)\left(\dfrac{7}{25}\right)=-\dfrac{96}{125}-\dfrac{21}{125}$. 5. This gives $-\dfrac{117}{125}$. Taking $\cos x$ as positive, forgetting that $x$ is obtuse, flips the sign. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 5: Trigonometry_