gaokao 2015 Q17

gaokao · China · hunan-science Trig Proofs Triangle Trigonometric Relation
17. (This question is worth 12 points) Let the sides opposite to angles $A, B, C$ of $\triangle ABC$ be $a, b, c$ respectively. Given $a = b \tan A$ and $B$ is an obtuse angle. (I) Prove: $\mathrm { B } - \mathrm { A } = \frac { \pi } { 2 }$ (II) Find the range of $\sin \mathrm { A } + \sin \mathrm { C }$. 
17. (This question is worth 12 points)\\
Let the sides opposite to angles $A, B, C$ of $\triangle ABC$ be $a, b, c$ respectively. Given $a = b \tan A$ and $B$ is an obtuse angle.\\
(I) Prove: $\mathrm { B } - \mathrm { A } = \frac { \pi } { 2 }$\\
(II) Find the range of $\sin \mathrm { A } + \sin \mathrm { C }$.
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