Question

[Nhẹ nhàng như gió]

sin²20^o+sin²30^o-sin²40^o-sin²50^o+sin²60^o+sin²70^o

Answer 1

[Lê Song Phương]

Sử dụng các công thức sau:

+) \(\alpha+\beta=90^0\Rightarrow\hept{\begin{cases}sin\alpha=cos\beta\\cos\alpha=sin\beta\end{cases}}\)

+) \(sin^2\alpha+cos^2\alpha=1\)

Như vậy \(sin^220^0+sin^230^0-sin^240^0-sin^250^0+sin^260^0+sin^270^0\)

\(=\left(sin^220^0+sin^270^0\right)+\left(sin^230^0+sin^260^0\right)-\left(sin^240+sin^250^0\right)\)

\(=\left(sin^220^0+cos^220^0\right)+\left(sin^230^0+cos^230^0\right)-\left(sin^240^0+cos^240^0\right)\)

\(=1+1-1=1\)