A) \[-\text{cosec }88{}^\circ \]
B) \[-\text{cosec 2}{}^\circ \]
C) \[-\text{cosec 44}{}^\circ \]
D) \[-\text{cosec 46}{}^\circ \]
Correct Answer: B
Solution :
\[\frac{\cot 224{}^\circ -\cot 134{}^\circ }{\cot 226{}^\circ +cot316{}^\circ }\] \[=\frac{\cot (180{}^\circ +44{}^\circ )-\cot (180{}^\circ -46{}^\circ )}{\cot (180{}^\circ +46{}^\circ )+cot(270{}^\circ +46){}^\circ }\] \[=\frac{\cot 44{}^\circ +\cot 46{}^\circ }{\cot 46{}^\circ -tan46{}^\circ }=\frac{tan46{}^\circ +tan44{}^\circ }{tan44{}^\circ -tan46{}^\circ }\] \[=\frac{\sin (46{}^\circ +44{}^\circ )}{\sin (44{}^\circ -46{}^\circ )}=-\cos ec2{}^\circ \]
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