gaokao 2015 Q17

gaokao · China · hunan-arts Trig Proofs Triangle Trigonometric Relation
17. (This question is worth 12 points) Let the sides opposite to angles $A , B , C$ of $\triangle A B C$ be $a , b , c$ respectively, with $a = b \tan A$. (I) Prove that: $\sin \mathrm { B } = \cos \mathrm { A }$ (II) If $\sin C - \sin A \cos B = \frac { 3 } { 4 }$ and $B$ is an obtuse angle, find $A$, $B$, and $C$.
17. (This question is worth 12 points)\\
Let the sides opposite to angles $A , B , C$ of $\triangle A B C$ be $a , b , c$ respectively, with $a = b \tan A$.\\
(I) Prove that: $\sin \mathrm { B } = \cos \mathrm { A }$\\
(II) If $\sin C - \sin A \cos B = \frac { 3 } { 4 }$ and $B$ is an obtuse angle, find $A$, $B$, and $C$.