A) 1
B) 2
C) 3
D) 100
Correct Answer: B
Solution :
\[\sin \theta +\text{cosec}\theta =2\Rightarrow \sin \theta +\frac{1}{\sin \theta }=2\] \[\Rightarrow \] \[{{\sin }^{2}}\theta -2\sin \theta +1=0\] \[\Rightarrow \] \[{{(\sin \theta -1)}^{2}}=0\] \[\Rightarrow \] \[\sin \theta =1\Rightarrow \text{cosec}\theta =1\] \[\therefore \]\[{{\sin }^{100}}\theta +\text{cose}{{\text{c}}^{100}}\theta =1+1=2\]
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