Giải thích các bước giải:

\[\begin{array}{l} b,\\ B = \dfrac{{\sin \left( {\pi  - a} \right).\cot \left( {\dfrac{\pi }{2} - a} \right).\cos \left( {2\pi  - a} \right)}}{{\tan \left( {\pi  + a} \right).\tan\left( {\dfrac{\pi }{2} + a} \right).\sin \left( { - a} \right)}}\\  = \dfrac{{\sin a.\dfrac{{\cos \left( {\dfrac{\pi }{2} - a} \right)}}{{\sin \left( {\dfrac{\pi }{2} - a} \right)}}.\cos \left( { - a} \right)}}{{\tan a\tan\left( {\pi  + \left( {a - \dfrac{\pi }{2}} \right)} \right).\left( { - \sin a} \right)}}\\  = \dfrac{{\sin a.\dfrac{{\sin a}}{{\cos a}}.\cos a}}{{\tan a.\tan\left( {a - \dfrac{\pi }{2}} \right).\left( { - \sin a} \right)}}\\  = \dfrac{{\sin a.\tan a.\cos a}}{{\tan a.\left( { - \tan \left( {\dfrac{\pi }{2} - a} \right)} \right).\left( { - \sin a} \right)}}\\  = \dfrac{{\cos a}}{{\tan \left( {\dfrac{\pi }{2} - a} \right)}} = \dfrac{{\cos a}}{{\dfrac{{\sin \left( {\dfrac{\pi }{2} - a} \right)}}{{\cos \left( {\dfrac{\pi }{2} - a} \right)}}}} = \dfrac{{\cos a}}{{\dfrac{{\cos a}}{{\sin a}}}} = \sin a\\ c,\\ C = \dfrac{{{{\sin }^2}\left( {\dfrac{{3\pi }}{2} + a} \right)}}{{{{\cot }^2}\left( {a - 2\pi } \right)}} + \dfrac{{{{\sin }^2}\left( { - a} \right)}}{{{{\cot }^2}\left( {a - \dfrac{{3\pi }}{2}} \right)}}\\  = \dfrac{{{{\sin }^2}\left( {2\pi  + \left( {a - \dfrac{\pi }{2}} \right)} \right)}}{{{{\cot }^2}a}} + \dfrac{{{{\sin }^2}a}}{{{{\cot }^2}\left( {a - \dfrac{\pi }{2}} \right)}}\\  = \dfrac{{{{\sin }^2}\left( {a - \dfrac{\pi }{2}} \right)}}{{{{\cot }^2}a}} + \dfrac{{{{\sin }^2}a}}{{\dfrac{{{{\cos }^2}\left( {a - \dfrac{\pi }{2}} \right)}}{{{{\sin }^2}\left( {a - \dfrac{\pi }{2}} \right)}}}}\\  = \dfrac{{{{\cos }^2}a}}{{\dfrac{{{{\cos }^2}a}}{{{{\sin }^2}a}}}} + \dfrac{{{{\sin }^2}a}}{{\dfrac{{{{\sin }^2}a}}{{{{\cos }^2}a}}}} = {\sin ^2}a + {\cos ^2}a = 1 \end{array}\]

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
b,\\
B = \dfrac{{\sin \left( {\pi  - a} \right).\cot \left( {\dfrac{\pi }{2} - a} \right).\cos \left( {2\pi  - a} \right)}}{{\tan \left( {\pi  + a} \right).tan\left( {\dfrac{\pi }{2} + a} \right).\sin \left( { - a} \right)}}\\
 = \dfrac{{\sin a.\dfrac{{\cos \left( {\dfrac{\pi }{2} - a} \right)}}{{\sin \left( {\dfrac{\pi }{2} - a} \right)}}.\cos \left( { - a} \right)}}{{\tan a.tan\left( {\pi  + \left( {a - \dfrac{\pi }{2}} \right)} \right).\left( { - \sin a} \right)}}\\
 = \dfrac{{\sin a.\dfrac{{\sin a}}{{\cos a}}.\cos a}}{{\tan a.tan\left( {a - \dfrac{\pi }{2}} \right).\left( { - \sin a} \right)}}\\
 = \dfrac{{\sin a.\tan a.\cos a}}{{\tan a.\left( { - \tan \left( {\dfrac{\pi }{2} - a} \right)} \right).\left( { - \sin a} \right)}}\\
 = \dfrac{{\cos a}}{{\tan \left( {\dfrac{\pi }{2} - a} \right)}} = \dfrac{{\cos a}}{{\dfrac{{\sin \left( {\dfrac{\pi }{2} - a} \right)}}{{\cos \left( {\dfrac{\pi }{2} - a} \right)}}}} = \dfrac{{\cos a}}{{\dfrac{{\cos a}}{{\sin a}}}} = \sin a\\
c,\\
C = \dfrac{{{{\sin }^2}\left( {\dfrac{{3\pi }}{2} + a} \right)}}{{{{\cot }^2}\left( {a - 2\pi } \right)}} + \dfrac{{{{\sin }^2}\left( { - a} \right)}}{{{{\cot }^2}\left( {a - \dfrac{{3\pi }}{2}} \right)}}\\
 = \dfrac{{{{\sin }^2}\left( {2\pi  + \left( {a - \dfrac{\pi }{2}} \right)} \right)}}{{{{\cot }^2}a}} + \dfrac{{{{\sin }^2}a}}{{{{\cot }^2}\left( {a - \dfrac{\pi }{2}} \right)}}\\
 = \dfrac{{{{\sin }^2}\left( {a - \dfrac{\pi }{2}} \right)}}{{{{\cot }^2}a}} + \dfrac{{{{\sin }^2}a}}{{\dfrac{{{{\cos }^2}\left( {a - \dfrac{\pi }{2}} \right)}}{{{{\sin }^2}\left( {a - \dfrac{\pi }{2}} \right)}}}}\\
 = \dfrac{{{{\cos }^2}a}}{{\dfrac{{{{\cos }^2}a}}{{{{\sin }^2}a}}}} + \dfrac{{{{\sin }^2}a}}{{\dfrac{{{{\sin }^2}a}}{{{{\cos }^2}a}}}} = {\sin ^2}a + {\cos ^2}a = 1
\end{array}\)