Question

The value of ${\sin }^2{5}^{\circ }+{\sin }^2{10}^{\circ }+{\sin }^2{15}^{\circ }......+{\sin }^2{90}^{\circ }$ is equal to

• A. $\frac{17}{2}$
• B. $\frac{19}{2}$
• C. $\frac{21}{2}$
• D. $\frac{23}{2}$

Answer 1

The correct option is B $\frac{19}{2}$

${\sin }^2{5}^{\circ }+{\sin }^2{10}^{\circ }+{\sin }^2{15}^{\circ }......+{\sin }^2{90}^{\circ }$

$=({\sin }^2{5}^o+{\sin }^2{85}^o)+({\sin }^2{10}^o+{\sin }^2{80}^o)+...........+({\sin }^2{45}^o+{\sin }^2{45}^o)+{\sin }^2{90}^o-{\sin }^2{45}^o$

$=({\sin }^2{5}^o+{\cos }^2{5}^o)+({\sin }^2{10}^o+{\cos }^2{10}^o)+...........+({\sin }^2{45}^o+{\cos }^2{45}^o)+{\sin }^2{90}^o-{\sin }^2{45}^o$

$=1+1+1+.......+1-\frac{1}{2}$

$=10-\frac{1}{2}=\frac{19}{2}$