A) 1
B) \[\frac{1}{2}\]
C) 2
D) 0
Correct Answer: C
Solution :
| [c] \[\sin \theta +\operatorname{cosec}\theta =2\] \[\Rightarrow \] \[\sin \theta +\frac{1}{\sin \theta }=2\] \[\Rightarrow \] \[{{\sin }^{2}}\theta +1=2\sin \theta \] \[\Rightarrow \] \[{{\sin }^{2}}\theta -2\sin \theta +1=0\] \[\Rightarrow \] \[{{(sin\theta -1)}^{2}}=0\] \[\Rightarrow \] \[\sin \theta =1=\sin 90{}^\circ \] \[\therefore \] \[\theta =90{}^\circ \] \[\therefore \] \[{{\sin }^{7}}\theta +\text{cose}{{\text{c}}^{7}}\theta =1+1=2\] |
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