A) 7
B) 8
C) 9
D) \[\frac{19}{2}\]
Correct Answer: D
Solution :
\[{{\sin }^{2}}5{}^\circ +{{\sin }^{2}}10{}^\circ +{{\sin }^{2}}15{}^\circ +.....+......+.....\] \[{{\sin }^{2}}75{}^\circ +{{\sin }^{2}}80{}^\circ +{{\sin }^{2}}85{}^\circ +{{\sin }^{2}}90{}^\circ \] \[\Rightarrow \,\,{{\sin }^{2}}5{}^\circ +{{\sin }^{2}}10{}^\circ +{{\sin }^{2}}15{}^\circ +.....{{\sin }^{2}}\] \[(90-15{}^\circ )+{{\sin }^{2}}(90-10)+si{{n}^{2}}(90-5)+1\] \[\Rightarrow \,\,{{\sin }^{2}}5+{{\sin }^{2}}10+{{\sin }^{2}}15{}^\circ +......+{{\cos }^{2}}15{}^\circ \]\[+\,\,{{\cos }^{2}}10{}^\circ +{{\cos }^{2}}5{}^\circ +1\] \[\Rightarrow \,\,\,\,\,(1+1+1+....8\,times)+si{{n}^{2}}45{}^\circ +1\] \[\Rightarrow \,\,8+\frac{1}{2}+1=\frac{19}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
