A) \[2\]
B) \[0\]
C) \[1\]
D) \[-1\]
Correct Answer: C
Solution :
\[\left( \frac{\cos {{58}^{o}}}{\sin {{32}^{o}}} \right)-\sqrt{3}\] \[\left( \frac{\cos {{38}^{o}}.\operatorname{cosec}{{52}^{o}}}{\tan {{15}^{o}}.\tan {{60}^{o}}.\tan {{75}^{o}}} \right)\] \[=2\left( \frac{\cos ({{90}^{o}}-{{32}^{o}})}{\sin {{32}^{o}}} \right)\] \[-\sqrt{3}\left( \frac{\cos {{38}^{o}}.\operatorname{cosec}({{90}^{o}}-{{38}^{o}})}{\tan {{15}^{o}}.\tan {{60}^{o}}.\tan ({{90}^{o}}-{{15}^{o}})} \right)\] \[=\frac{2\sin {{32}^{o}}}{\sin {{32}^{o}}}-\sqrt{3}\left( \frac{\cos {{38}^{o}}.\sec {{38}^{o}}}{\tan {{15}^{o}}\times \sqrt{3}\times \cot {{15}^{o}}} \right)\] \[=2-\frac{\sqrt{3}}{\sqrt{3}}=2-1=1\] \[[\because \,\,\cos \theta .\sec \theta =1\tan \theta .\cot \theta =1]\]
You need to login to perform this action.
You will be redirected in
3 sec
