a) \(\cos a =  - \sqrt {1 - {{\sin }^2}a}  =  - \frac{4}{5}\left( {\frac{\pi }{2} < a < \pi } \right)\)

\(\sin \left( {a + \frac{\pi }{4}} \right) = \sin \frac{\pi }{4}.\cos a + \cos \frac{\pi }{4}.\sin a = \frac{{ - \sqrt 2 }}{{10}}\)

b) \(A = \frac{{2\sin 3x.\cos 2x + 2\sin 3x}}{{2\cos 3x.\cos 2x + 2\cos 3x}} = \frac{{2\sin 3x.\left( {\cos 2x + 1} \right)}}{{2\cos 3x.\left( {\cos 2x + 1} \right)}} = \tan 3x\)

c) \(VT = \frac{{1 - 2\sin x.\cos x}}{{{{\cos }^2}x - {{\sin }^2}x}} = \frac{{{{\left( {\cos x - \sin x} \right)}^2}}}{{\left( {\cos x - \sin x} \right)\left( {\cos x + \sin x} \right)}}\)

\( = \frac{{\cos x - \sin x}}{{\cos x + \sin x}} = \frac{{1 - \tan x}}{{1 + \tan x}} = VP\)