3. In $\triangle A B C$, it is known that $\sin A=10 \sin B \sin C, \cos A=10 \cos B \cos C$, then the value of $\tan A$ is $\qquad$
Answer 11.
Solution: Since $\sin A-\cos A=10(\sin B \sin C-\cos B \cos C)=-10 \cos (B+C)=10 \cos A$, we have $\sin A=11 \cos A$, thus $\tan A=11$.