0\; \; \to \; \; cosa=+\sqrt{1-\frac{16}{25}}=\frac{3}{5}\\\\cos\beta =-\frac{5}{13}\; \; \to \; \; sina=\pm \sqrt{1-cos^2a}\\\\\pi <\beta <\frac{3\pi }{2}\; \; \to \; \; sin\beta <0\; \; \to \; \; sin\beta =-\sqrt{1-\frac{25}{169}}=-\frac{12}{13}\\\\cos(a+\beta )=cosa\, cos\beta-sina\. sin\beta =-\frac{3}{5}\cdot \frac{5}{13}+\frac{4}{5}\cdot \frac{12}{13}=\frac{33}{65}" alt="1)\; \; sina=\frac{4}{5}\; \; ,\; \; cosa=\pm \sqrt{1-sin^2a}\\\\0<a<\frac{\pi }{2}\; \; \to \; \; cos>0\; \; \to \; \; cosa=+\sqrt{1-\frac{16}{25}}=\frac{3}{5}\\\\cos\beta =-\frac{5}{13}\; \; \to \; \; sina=\pm \sqrt{1-cos^2a}\\\\\pi <\beta <\frac{3\pi }{2}\; \; \to \; \; sin\beta <0\; \; \to \; \; sin\beta =-\sqrt{1-\frac{25}{169}}=-\frac{12}{13}\\\\cos(a+\beta )=cosa\, cos\beta-sina\. sin\beta =-\frac{3}{5}\cdot \frac{5}{13}+\frac{4}{5}\cdot \frac{12}{13}=\frac{33}{65}" align="absmiddle" class="latex-formula">
