Question

The value of ${\sin }^2{5}^o+{\sin }^2{10}^o+{\sin }^2{15}^o+...+{\sin }^2{85}^o+{\sin }^2{90}^o$ is?

• A. $7$
• B. $8$
• C. $9.5$
• D. $10$

Answer 1

Answer: (C)

$9.5$

$si{n}^{2}5°+si{n}^{2}10°+si{n}^{2}15°+.......+si{n}^{2}90°$

$5+10+15+......+90$

$a=5$ $d=5$

$=>5+(n-1)5=90$

$=>5n-5+5=90$

$=>n=18$

$si{n}^{2}45°=\frac{1}{2}$ $si{n}^{2}90°=1$

$si{n}^{2}5°+si{n}^{2}85°=1$

$si{n}^{2}10°+si{n}^{2}80°=1$

$si{n}^{2}40°+si{n}^{2}50°=1$

Sum of the series is $[8+1+\frac{1}{2}]$

$=9.5$