A) \[1\]
B) \[2\]
C) \[3\]
D) \[0\]
Correct Answer: A
Solution :
\[2\left( \frac{\cos {{58}^{o}}}{\sin {{32}^{o}}} \right)-\sqrt{3}\] \[\left( \frac{\cos {{38}^{o}}\operatorname{cosec}{{52}^{o}}}{\tan {{15}^{o}}\tan {{60}^{o}}\tan {{75}^{o}}} \right)\] \[=2\left\{ \frac{\cos ({{90}^{o}}-{{32}^{o}})}{\sin {{32}^{o}}} \right\}-\]\[\sqrt{3}\left\{ \frac{\cos {{38}^{o}}\operatorname{cosec}({{90}^{o}}-{{38}^{o}})}{\tan {{15}^{o}}\tan {{60}^{o}}\tan ({{90}^{o}}-{{15}^{o}})} \right\}\] \[=2\left( \frac{\sin {{32}^{o}}}{\sin {{32}^{o}}} \right)-\sqrt{3}\] \[\left\{ \frac{\cos {{38}^{o}}\sec {{38}^{o}}}{\tan {{15}^{o}}\times \sqrt{3}\times \cot {{15}^{o}}} \right\}\] \[=2-\sqrt{3}\left\{ \frac{\cos {{38}^{o}}\times \frac{1}{\cos {{38}^{o}}}}{\tan {{15}^{o}}\times \sqrt{3}\times \frac{1}{\tan {{15}^{o}}}} \right\}\] \[=2-\frac{\sqrt{3}}{\sqrt{3}}=2-1=1\]
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