Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
G = \cos \left( {270^\circ - \alpha } \right) - 2\sin \left( {\alpha - 450^\circ } \right) + \cos \left( {\alpha + 900^\circ } \right) + 2\sin \left( {270^\circ - \alpha } \right)\\
+ \cos \left( {450^\circ - \alpha } \right)\\
= \cos \left( {360^\circ - \left( {\alpha + 90^\circ } \right)} \right) - 2\sin \left( {\left( {\alpha - 90^\circ } \right) - 360^\circ } \right)\\
+ \cos \left( {\left( {\alpha + 180^\circ } \right) + 2.360^\circ } \right) + 2\sin \left( {360^\circ - \left( {\alpha + 90^\circ } \right)} \right) + \cos \left( {360^\circ + \left( {90^\circ - \alpha } \right)} \right)\\
= \cos \left( { - \left( {\alpha + 90^\circ } \right)} \right) - 2\sin \left( {\alpha - 90^\circ } \right) + \cos \left( {\alpha + 180^\circ } \right)\\
+ 2\sin \left( { - \left( {\alpha + 90^\circ } \right)} \right) + \cos \left( {90^\circ - \alpha } \right)\\
= \cos \left( {\alpha + 90^\circ } \right) - 2\cos \left( {90^\circ - \left( {\alpha - 90^\circ } \right)} \right)\\
- \cos \left( {180^\circ - \left( {\alpha + 180^\circ } \right)} \right) - 2\sin \left( {\alpha + 90^\circ } \right) + \sin \alpha \\
= \sin \left( { - \alpha } \right) - 2\cos \left( {180^\circ - \alpha } \right) - \cos \left( { - \alpha } \right)\\
- 2\cos \left( {90^\circ - \left( {\alpha + 90^\circ } \right)} \right) + \sin \alpha \\
= - \sin \alpha + 2\cos \alpha - \cos \alpha - 2\cos \alpha + \sin \alpha \\
= - \cos \alpha \\
L,\\
\tan x = \frac{{\sin x}}{{\cos x}} = \frac{{\cos \left( {90^\circ - x} \right)}}{{\sin \left( {90^\circ - x} \right)}} = \cot \left( {90^\circ - x} \right)\\
L = \frac{{\left( {\cot 44^\circ + \tan 226^\circ } \right).\cos 406^\circ }}{{\cos 316^\circ }} - \cot 72^\circ .\cot 18^\circ \\
= \frac{{\left( {\cot 44^\circ + \tan \left( {180^\circ + 46^\circ } \right)} \right).cos\left( {360^\circ + 46^\circ } \right)}}{{\cos \left( {360^\circ - 44^\circ } \right)}} - \cot 72^\circ .\tan \left( {90^\circ - 18^\circ } \right)\\
= \frac{{\left( {\tan \left( {90^\circ - 44^\circ } \right) + \tan 46^\circ } \right).cos46^\circ }}{{\cos 44^\circ }} - \cot 72^\circ .\tan 72^\circ \\
= \frac{{2\tan 46^\circ .\cos 46^\circ }}{{\sin \left( {90^\circ - 44^\circ } \right)}} - 1\\
= \frac{{2\sin 46^\circ }}{{\sin 46^\circ }} - 1\\
= 2 - 1 = 1
\end{array}\)
