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\(B=\sin^247^o\times\cos45^o+\sin45^o\times\cos^247^o\)
\(B=\sin^247^o\times\cos45^o+\cos45^o\times\cos^247^o\)
\(B=\cos45^o\left(\sin^247^o+\cos^247^o\right)\)
\(B=\cos45^o.1=\cos45^o\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=2008\left(\sin^220^o+\cos^220^o\right)+\cos70^o-\cos70^o+\frac{\sin20^o}{\cos20}.\frac{sin70}{c\text{os}70}\)
\(=2008+1=2009\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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Chú ý 2 điều: \(\cos45^o=\sin45^o=\frac{\sqrt{2}}{2}\) và \(\cos^2a+\sin^2a=1\)
Do đó:
a) \(A=\cos^252^o.\frac{\sqrt{2}}{2}+\sin^252^o.\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\left(\cos^252^o+\sin^252^o\right)=\frac{\sqrt{2}}{2}.1=\frac{\sqrt{2}}{2}\)
b) \(B=\frac{\sqrt{2}}{2}.\cos^247^o+\frac{\sqrt{2}}{2}.\sin^247^o=\frac{\sqrt{2}}{2}\left(\cos^247^o+\sin^247^o\right)=\frac{\sqrt{2}}{2}.1=\frac{\sqrt{2}}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\left(1-sin^247^0\right)\cdot sin45^0+sin47^0\cdot\left(1-sin^245^0\right)\)
\(=sin45-sin^247^0\cdot\dfrac{\sqrt{2}}{2}+sin47^0-\dfrac{1}{2}\cdot sin47^0\)
\(\simeq0.69\)
\(D=\cos45^0\cdot\cos^223^0+\sin45^0\cdot\cos^267^0\)
\(=\dfrac{\sqrt{2}}{2}\left(\cos^223^0+\cos^267^0\right)\)
\(=\dfrac{\sqrt{2}}{2}\)