a) \(VT = {{\cos a\cos b+\sin a\sin b}\over{\cos a\cos b-\sin a\sin b}}\)

\(=\frac{\frac{\cos a\cos b}{\sin a\sin b}+1}{\frac{\cos a\cos b}{\sin a\sin b}-1}\)

\(=\frac{\cot a\cot b+1}{\cot a\cot b-1}=VP\)

b)      \(VT = [\sin a\cos b + \cos a\sin b][\sin a\cos b - \cos a\sin a]\)

\(= (\sin a\cos b)^2– (\cos a\sin b)^2\)

\(=sin^2\,a\,cos^2\,b-cos^2\,a\,sin^2\,b\)

\(= \sin^2 a(1 – \sin^2 b) – (1 – \sin^2 a)\sin^2 b\)

\(= \sin^2a – \sin^2b \)

\(= \cos^2b( 1– \cos^2a) – \cos^2 a(1 – \cos^2 b) \)

\(=  \cos^2 b – \cos^2 a\)

c.\(VT= (\cos a\cos b - \sin a\sin b)(\cos a\cos b + \sin a\sin b)\)

\(= (\cos a\cos b)^2 – (\sin a\sin b)^2\)           

\(= \cos^2 a(1 – \sin^2 b) – (1 – \cos^2 a)\sin^2 b \)

\(= \cos^2 a – \sin^2 b\)

\(= \cos^2 b(1 – \sin^2 a) – (1 – \cos^2 b)\sin^2 a \)

\(= \cos^2 b – \sin^2 a\)