Find the exact value of $$\cot(v-u)$$ given that $\sin u=−3/5$ and $\cos v = − 7/25$ (Both $u$ and $v$ are in Quadrant III.)
Do you know a formula relating the cotangent to the sine and cosine?
Do you know formulas relating $\sin(A+B)$ and $\cos(A+B)$ to $\sin A,\sin B,\cos A, \cos B$?
Do you know a formula relating $\sin C$ and $\cos C$?
Do you know which trig functions are positive in which quadrants?
Hint: Apply $$\sin(A+B)=\sin A \cos B+\cos A \sin B$$ $$\cos(A+B)=\cos A \cos B- \sin A \sin B$$