A) \[0\]
B) \[1\]
C) \[-1~\]
D) \[2\]
Correct Answer: A
Solution :
| [a] Given, \[\sin \theta +{{\sin }^{2}}\theta =1\] \[\Rightarrow \] \[\sin \theta =1-{{\sin }^{2}}\theta \] \[\Rightarrow \] \[\sin \theta ={{\cos }^{2}}\theta \] (i) \[{{\cos }^{12}}\theta +3{{\cos }^{10}}\theta +3\,co{{s}^{8}}\theta +{{\cos }^{6}}\theta -1\] \[={{(co{{s}^{4}}\theta +co{{s}^{2}}\theta )}^{3}}-1\] \[={{(si{{n}^{2}}\theta +co{{s}^{2}}\theta )}^{2}}-1\] \[={{(1)}^{2}}-1=0\] |
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