\(\begin{array}{l}
4)\,a)\,A = \frac{{\cos 41^\circ }}{{\sin 49^\circ }} + \tan 28^\circ .\tan 62^\circ \\
= \frac{{\sin 49^\circ }}{{\sin 49^\circ }} + \tan 28^\circ .\cot 28^\circ \\
= 1 + 1 = 2\\
b)\,B = {\cos ^2}10^\circ + {\cos ^2}20^\circ + {\cos ^2}70^\circ + {\cos ^2}80^\circ \\
= {\cos ^2}10^\circ + {\sin ^2}10^\circ + {\cos ^2}20^\circ + {\sin ^2}20^\circ \\
= 1 + 1 = 2\\
c)\,C = 9{\sin ^2}\alpha + 24\sin \alpha \cos \alpha + 16{\cos ^2}\alpha + 16{\sin ^2}\alpha - 24\sin \alpha \cos \alpha + 9{\cos ^2}\alpha \\
= 25\left( {{{\sin }^2}\alpha + {{\cos }^2}\alpha } \right) = 25.1 = 25
\end{array}\)
