The value of sin21∘+sin22∘+sin22∘+...+sin289∘+sin290∘
As we know that sin2θ+cos2θ=1 .....(i)
and also cosθ=sin(90−θ)........(ii)
Substitute equation(ii) in equation(i), we get
sin2θ+sin2(90−θ)=1.........(iii)
Given sin21∘+sin22∘+sin22∘+...+sin289∘+sin290∘
=(sin21+sin289)+(sin22+sin288)+....+(sin244+sin246)+(sin245+sin290)
=(sin21+sin2(90−1))+(sin2+sin2(90−2))+....+(sin244+sin2(90−44))+(sin245+sin290)
=1+1......(44times)+(1√2)2+1
[From equation(iii)]
=45+12
=45.5
Therefore, the correct option is D (45.5)