| The minimum value of \[2{{\sin }^{2}}\theta +3{{\cos }^{2}}\theta \]is [SSC (CPO) 2011] |
A) 0
B) \[3\]
C) \[2\]
D) \[1\]
Correct Answer: B
Solution :
| \[2{{\sin }^{2}}\theta +3{{\cos }^{2}}\theta =2{{\sin }^{2}}\theta +2{{\cos }^{2}}\theta +{{\cos }^{2}}\theta \] |
| \[=2\,\,({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )+{{\cos }^{2}}\theta \] |
| \[=2+{{\cos }^{2}}\theta \] |
| \[\because \]Minimum value of \[\theta =-1\] |
| \[\therefore \]Required minimum value \[=2+{{(-1)}^{2}}=2+1=3\] |
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