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\(A=\dfrac{\sqrt{2}}{2}\cdot\cos^252^0+\dfrac{\sqrt{2}}{2}\cdot\sin^252^0\)
\(=\dfrac{\sqrt{2}}{2}\left(\cos^252^0+\sin^252^0\right)\)
\(=\dfrac{\sqrt{2}}{2}\)
sin 39 ° 13 ' ≈ 0,6323 cos 52 ° 18 ' ≈ 0,6115
tg 13 ° 20 ' ≈ 0,2370 cotg 10 ° 17 ' ≈ 0,5118
sin 45 ° ≈ 0,7071 cos 45 ° ≈ 0,7071
a: \(=\dfrac{\sqrt{2}}{2}\left(cos^252^0+sin^252^0\right)=\dfrac{\sqrt{2}}{2}\)
b: \(=\dfrac{\sqrt{2}}{2}\left(cos^247^0+sin^247^0\right)=\dfrac{\sqrt{2}}{2}\)
a) \(\sin25^017'=\cos64^043'\)
b) \(\cos43^019'=\sin46^041'\)
c) \(\tan55^037'=\cot34^023'\)
d) \(\cot41^049'=\tan48^011'\)
\(A=\frac{1-2sina.cosa}{sin^2a-cos^2a}=\frac{sin^2a+cos^2a-2sina.cosa}{\left(sina-cosa\right)\left(sina+cosa\right)}=\frac{\left(sina-cosa\right)^2}{\left(sina-cosa\right)\left(sina+cosa\right)}=\frac{sina-cosa}{sina+cosa}\)
b/ \(A=\frac{\frac{sina}{cosa}-\frac{cosa}{cosa}}{\frac{sina}{cosa}+\frac{cosa}{cosa}}=\frac{tana-1}{tana+1}=\frac{\frac{1}{3}-1}{\frac{1}{3}+1}=-\frac{1}{2}\)
1) \(\cot51^0=\tan39^0\)
\(\cot79^015'=\tan10^045'\)
Do đó: \(\cot79^015'< \tan13^0< \tan28^0< \cot51^0< \tan47^0\)
2) \(\cos62^0=\sin28^0\)
\(\cos63^041'=\sin26^019'\)
\(\cos87^0=\sin3^0\)
Do đó: \(\cos87^0< \cos63^041'< \cos62^0< \sin47^0< \sin50^0\)
\(A=\cos^252^0\cdot\sin45^0+\sin^252^0\cdot\cos45^0\)
\(=\dfrac{\sqrt{2}}{2}\left(\cos^252^0+\sin^252^0\right)=\dfrac{\sqrt{2}}{2}\)