Тригонометрия 10 класс

Решите задачу:

$cos^2a=?\; \; \; \; \; \frac{sin3a}{sina} +\frac{cos3a}{cosa} =1\\\\ \frac{sin3a}{sina} + \frac{cos3a}{cosa} = \frac{sin3a\cdot cosa+cos3a\cdot sina}{sina\cdot cosa} = \frac{sin(3a+a)}{\frac{1}{2}sin2a} = \frac{2sin4a}{sin2a} =\\\\= \frac{2\cdot 2sin2a\cdot cos2a}{sin2a} =4cos2a\\\\4cos2a=1\; \; \; \Rightarrow \; \; \; cos2a=\frac{1}{4}\\\\Formyla:\; \; cos2a=2cos^2a-1\; \; \Rightarrow \; \; cos^2a=\frac{1+cos2a}{2}\\\\cos^2a= \frac{1+\frac{1}{4}}{2}= \frac{5}{4\cdot 2} = \frac{5}{8}$