A) \[1\]
B) \[\frac{1}{2}\]
C) \[2\]
D) \[3\]
Correct Answer: A
Solution :
| [a] Given, \[\sin A+{{\sin }^{2}}A=1\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\sin A=1-{{\sin }^{2}}A={{\cos }^{2}}A\] \[[{{\cos }^{2}}A+{{\sin }^{2}}A=1]\] |
| On squaring both sides, we get |
| \[{{\sin }^{2}}A={{\cos }^{4}}A\] |
| \[\Rightarrow \,\,\,\,\,\,1-{{\cos }^{2}}A={{\cos }^{4}}A\,\,\,\,\,\,\Rightarrow \,\,\,\,\,{{\cos }^{2}}A+{{\cos }^{4}}A=1\] |
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