a) Ta có: \(\cos 14^{\circ}=\sin(90^o - 14^o)=\sin 76^{\circ}\);
\(\cos 87^{\circ}=\sin (90^o - 87^o)=\sin 3^{\circ}.\).
Vì \( 3^o < 47^o < 76^o < 78^o\)
\(\Rightarrow \sin 3^{\circ}< \sin 47^{\circ}< \sin 76^{\circ}< \sin 78^{\circ}\)
\(\Rightarrow \cos 87^{\circ}< \sin 47^{\circ}< \cos 14^{\circ} < \sin 78^o\).
b) Ta có: \(\cot 25^{\circ}=\tan (90^o - 25^o)=\tan 65^{\circ}; \)
\(\cot 38^{\circ}=\tan (90^o - 38^o)=\tan 52^{\circ}\).
Vì \(52^o < 62^o < 65^o < 73^o\)
\(\Rightarrow \tan 52^{\circ}< \tan 62^{\circ}< \tan 65^{\circ}< \tan 73^{\circ}\);
\(\Rightarrow \cot 38^{\circ}< \tan 62^{\circ}< \cot 25^{\circ}< \tan 73^{\circ}\).
