Đáp án: $S=\dfrac{17}2$
Giải thích các bước giải:
Ta có:
$S=\sin^2(5^o)+\sin^2(10^o)+\sin^2(15^o)+....+\sin^2(85^o)$
$\to S=\sin^2(85^o)+\sin^2(80^o)+\sin^2(75^o)+....+\sin^2(5^o)$
$\to S+S=(\sin^2(5^o)+\sin^2(85^o))+(\sin^2(10^o)+\sin^2(80^o))+...+(\sin^2(85^o)+\sin^2(5^o))$
$\to S+S=(\sin^2(5^o)+\cos^2(90^o-85^o))+(\sin^2(10^o)+\cos^2(90^o-80^o))+...+(\sin^2(85^o)+\cos^2(90^o-5^o))$
$\to 2S=(\sin^2(5^o)+\cos^2(5^o))+(\sin^2(10^o)+\cos^2(10^o))+...+(\sin^2(85^o)+\cos^2(85^o))$
$\to 2S=1+1+...+1$ có $17$ số hạng $1$
$\to 2S=17$
$\to S=\dfrac{17}2$
