Sum and Difference Identities · Exercise 20

Find the requested information.

Given that $sina=\frac{2}{3}$ and $cosb=-\frac{1}{4},$ with $a$ and $b$ both in the interval $\left[\frac{\pi }{2},\pi \right),$ find $sin\left(a+b\right)$ and $cos\left(a-b\right).$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §9.2 Sum and Difference Identities · Exercise 20