Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
C = \cos \left( {5\pi - x} \right) - \sin \left( {\frac{{3\pi }}{2} + x} \right) + \tan \left( {\frac{{3\pi }}{2} - x} \right) + \cot \left( {3\pi - x} \right)\\
= \cos \left( {4\pi + \left( {\pi - x} \right)} \right) - \sin \left( {2\pi + \left( {x - \frac{\pi }{2}} \right)} \right) + \tan \left( {\pi + \left( {\frac{\pi }{2} - x} \right)} \right) + \cot \left( {3\pi - x} \right)\\
= \cos \left( {\pi - x} \right) - \sin \left( {x - \frac{\pi }{2}} \right) + \tan \left( {\frac{\pi }{2} - x} \right) + \cot \left( { - x} \right)\\
= - \cos x - \cos \left( {\frac{\pi }{2} - \left( {x - \frac{\pi }{2}} \right)} \right) + \frac{{\sin \left( {\frac{\pi }{2} - x} \right)}}{{\cos \left( {\frac{\pi }{2} - x} \right)}} + \frac{{\cos \left( { - x} \right)}}{{\sin \left( { - x} \right)}}\\
= - \cos x - \cos \left( {\pi - x} \right) + \frac{{\cos x}}{{\sin x}} + \frac{{\cos x}}{{ - \sin x}}\\
= - \cos x + \cos x + \cot x - \cot x\\
= 0\\
A = 2\cos x + 3\cos \left( {\pi - x} \right) - \sin \left( {\frac{{7\pi }}{2} - x} \right) + \tan \left( {\frac{{3\pi }}{2} - x} \right)\\
= 2\cos x - 3\cos x - \sin \left( {4\pi - \left( {x + \frac{\pi }{2}} \right)} \right) + \tan \left( {\pi + \left( {\frac{\pi }{2} - x} \right)} \right)\\
= - \cos x - \sin \left( { - x - \frac{\pi }{2}} \right) + \tan \left( {\frac{\pi }{2} - x} \right)\\
= - \cos x - \cos \left( {\frac{\pi }{2} - \left( { - x - \frac{\pi }{2}} \right)} \right) + \frac{{\sin \left( {\frac{\pi }{2} - x} \right)}}{{\cos \left( {\frac{\pi }{2} - x} \right)}}\\
= - \cos x - \cos \left( {\pi + x} \right) + \frac{{\cos x}}{{\sin x}}\\
= - \cos x + \cos \left( { - x} \right) + \cot x\\
= - \cos x + \cos x + \cot x\\
= \cot x
\end{array}\)
