A) \[8\frac{1}{2}\]
B) 9
C) \[9\frac{1}{2}\]
D) \[4\frac{1}{2}\]
E) 0
Correct Answer: C
Solution :
\[si{{n}^{2}}5{}^\circ +si{{n}^{2}}10{}^\circ \text{ +}si{{n}^{2}}15{}^\circ +...+si{{n}^{2}}90{}^\circ \] \[=si{{n}^{2}}5{}^\circ +si{{n}^{2}}10{}^\circ \text{ +}........\text{+}si{{n}^{2}}45{}^\circ +...\] \[+si{{n}^{2}}80{}^\circ +si{{n}^{2}}85{}^\circ \text{ +}si{{n}^{2}}90{}^\circ \] \[=si{{n}^{2}}5{}^\circ +si{{n}^{2}}10{}^\circ \text{ +}....\text{+}\frac{1}{2}+....+{{\cos }^{2}}10{}^\circ \] \[+{{\cos }^{2}}5{}^\circ +{{\sin }^{2}}90{}^\circ \] \[=({{\sin }^{2}}5{}^\circ +{{\cos }^{2}}5{}^\circ )+({{\sin }^{2}}10{}^\circ +{{\cos }^{2}}10{}^\circ )+\] \[.....+({{\sin }^{2}}40{}^\circ +{{\cos }^{2}}40{}^\circ )+{{\sin }^{2}}45{}^\circ \] \[+{{\sin }^{2}}90{}^\circ \] \[=1+1+1+1+1+1+1+1+\frac{1}{2}+1\] \[=9\frac{1}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
