The value of sin22° + sin24° + sin26° + ........ + sin290° is?

Answer: Option A

$$\begin{array}{rl}& \text{According to the question,}\\ & {\sin }^2{2}^{\circ }+{\sin }^2{4}^{\circ }+{\sin }^2{6}^{\circ }+.....+{\sin }^{2}90^{\circ }\\ & \text{Number of terms}\\ & =\frac{l-a}{d}+1\\ & =\frac{90-2}{2}+1\\ & =45\\ & \text{But }{\sin }^{2}90^{\circ }=1\\ & \text{So, 22 pairs}+{\sin }^{2}90^{\circ }\\ & =22+1\\ & =23\end{array}$$