A) \[{{90}^{{}^\circ }}\]
B) \[{{30}^{{}^\circ }}\]
C) \[{{45}^{{}^\circ }}\]
D) \[{{60}^{{}^\circ }}\]
Correct Answer: C
Solution :
(c): \[tan(x+y)=\sqrt{3}=tan{{60}^{{}^\circ }}\] \[\Rightarrow x+y={{60}^{{}^\circ }}\] ....(i) \[tan\left( x-y \right)=\frac{1}{\sqrt{3}}=tan{{30}^{{}^\circ }}\] \[\Rightarrow x-y={{30}^{{}^\circ }}\] .....(ii) \[\therefore x+y+x-y={{60}^{{}^\circ }}+{{30}^{{}^\circ }}\] \[\Rightarrow 2x={{90}^{{}^\circ }}\] \[\Rightarrow x=\frac{{{90}^{{}^\circ }}}{2}={{45}^{{}^\circ }}\]You need to login to perform this action.
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