$\begin{array}{l} 1)\sin a\cos b - \sin \left( {\pi - a} \right)\cos \left( { - b} \right)\\ = \sin a\cos b - \sin a\cos b = 0\\ 3)\tan \left( {\pi + 2a} \right)\tan \left( {\dfrac{\pi }{2} - 2a} \right)\\ = \tan 2a.\cot 2a = 1\\ 4)\cos a\sin \left( {\dfrac{\pi }{2} - a} \right) + \sin \left( {\pi - a} \right)\sin \left( {\pi + a} \right)\\ = \cos a.\cos a + \sin a.\left( { - \sin a} \right)\\ = {\cos ^2}a - {\sin ^2}a\\ = \cos 2a \end{array}$
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