A) 25
B) 4
C) Does not exist
D) None of the above
Correct Answer: D
Solution :
\[4{{\sin }^{2}}x-12\sin x+7\] \[=4({{\sin }^{2}}x-3\sin x)+7\] \[=4\left[ {{\left( \sin x-\frac{3}{2} \right)}^{2}}-\frac{9}{4} \right]+7\] \[=4{{\left( \sin x-\frac{3}{2} \right)}^{2}}-2\] Since, \[-1\le \sin x\le 1\] \[\therefore \] \[-\frac{5}{2}\le \sin x-\frac{3}{2}\le -\frac{1}{2}\] \[\Rightarrow \] \[\frac{1}{4}\le {{\left( \sin x-\frac{3}{2} \right)}^{2}}\le \frac{25}{4}\] \[\Rightarrow \] \[1\le 4{{\left( \sin x-\frac{3}{2} \right)}^{2}}\le 25\] \[\Rightarrow \] \[-1\le 4{{\left( \sin x-\frac{3}{2} \right)}^{2}}-2\le 23\]
You need to login to perform this action.
You will be redirected in
3 sec
