A) \[{{60}^{o}},{{0}^{o}},{{30}^{o}}\]
B) \[{{30}^{o}},{{60}^{o}},{{90}^{o}}\]
C) \[{{60}^{o}},{{30}^{o}},{{0}^{o}}\]
D) \[{{0}^{o}},{{60}^{o}},{{30}^{o}}\]
Correct Answer: C
Solution :
We have, \[\sin (A+B+C)=1\] \[\Rightarrow \] \[\sin (A+B+C)=\sin {{90}^{o}}\] \[\Rightarrow \] \[A+B+C={{90}^{o}}\] ?.(i) Also, \[\tan (A-B)=\frac{1}{\sqrt{3}}=\tan {{30}^{o}}\] \[\Rightarrow \] \[A-B={{30}^{o}}\] ?.(ii) and \[\sec \,(A+C)=2=sec{{60}^{o}}\] \[\Rightarrow \] \[A+C={{60}^{o}}\] ?.(iii) From (i) and (iii), we get \[B+C={{30}^{o}}\] ?(iv) From (i) and (iv), we get, \[A={{60}^{o}}\] \[\therefore \] \[B={{30}^{o}}\] [using \[A={{60}^{o}}\]in (ii)] and \[C={{0}^{o}}\] [using \[A={{60}^{o}}\]in (iii)]
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