Question

What is the value of $si{n}^{2}0+si{n}^2+$ _______ $+si{n}^{2}90$ ?

• A. $0$
• B. $45$
• C. $\frac{89}{2}$
• D. $\frac{91}{2}$

Answer 1

Answer: (C)

$\frac{89}{2}$

We have to find the value of $si{n}^{2}0+si{n}^{2}1+.........+si{n}^{2}90$

We have $si{n}^{2}90=co{s}^{2}0$ , $si{n}^{2}89=co{s}^{2}1$ , ............ , $si{n}^{2}46=co{s}^{2}44$ and $si{n}^{2}45=\frac{1}{2}$

Therefore the equation will reduce to $(si{n}^{2}0+co{s}^{2}0)+(si{n}^{2}1+co{s}^{2}1)+...........(si{n}^{2}44+co{s}^{2}44)+\frac{1}{2}=44+\frac{1}{2}=\frac{89}{2}$

Therefore option $C$ is correct