Question

The value of ${\sin }^2{15}^{\circ }+{\sin }^2{30}^{\circ }+{\sin }^2{45}^{\circ }+{\sin }^2{60}^{\circ }+{\sin }^2{75}^{\circ }$ is

• A. $1$
• B. $\frac{3}{2}$
• C. $\frac{5}{2}$
• D. $3$

Answer 1

The correct option is C $\frac{5}{2}$

$({\sin }^2{75}^0+{\sin }^2({15}^0\left)\right)+({\sin }^2{30}^0+{\sin }^2{60}^0)+{\sin }^2{45}^0$

$=({\cos }^2{15}^0+{\sin }^2{15}^0)+({\cos }^2{60}^0+{\sin }^2{60}^0)+\frac{1}{2}$

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

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

$=\frac{5}{2}$