gaokao 2019 Q17

gaokao · China · national-I-science 12 marks Trig Proofs Triangle Trigonometric Relation
17. (12 points) In $\triangle A B C$, the angles $A , B , C$ have opposite sides $a , b , c$ respectively. Given $( \sin B - \sin C ) ^ { 2 } = \sin ^ { 2 } A - \sin B \sin C$.
(1) Find $A$;
(2) If $\sqrt { 2
Solution:
17. (12 points)\\
In $\triangle A B C$, the angles $A , B , C$ have opposite sides $a , b , c$ respectively. Given $( \sin B - \sin C ) ^ { 2 } = \sin ^ { 2 } A - \sin B \sin C$.\\
(1) Find $A$;\\
(2) If $\sqrt { 2