Задача 78507 решите тригонометрические выражения...
Условие
Решение
[m]= \sin^2 a - 2\sin a \cos a + \cos^2 a + 2\sin a \cos a = \sin^2 a + \cos^2 a = 1[/m]
5.2. [m]\frac{(1-\cos a)(1 + \cos a)}{\sin a} = \frac{1-\cos^2 a}{\sin a} = \frac{\sin^2 a}{\sin a}= \sin a[/m]
5.10. [m](\cos^2 a + ctg^2 a + \sin^2 a) \cdot \sin^2 a = [/m]
[m]= (1+\frac{\cos^2 a}{\sin^2 a}) \cdot \sin^2 a = \sin^2 a + \cos^2 a = 1[/m]
511. [m]\cos^2 a - \cos^4 a + \sin^4 a = \cos^2 a + (\sin^2 a + \cos^2 a)(\sin^2 a - \cos^2 a) =[/m]
[m]= \cos^2 a + 1(\sin^2 a - \cos^2 a) = \cos^2 a + \sin^2 a - \cos^2 a = \sin^2 a[/m]
5.12. [m](\sin^2 a + tg^2 a\sin^2 a) \cdot ctg\ a = \sin^2 a(1 + tg^2 a) \cdot \frac{\cos a}{\sin a} =[/m]
[m]= \sin a \cdot (1+ \frac{\sin^2 a}{\cos^2 a}) \cdot \cos a =\sin a \cdot \cos a \cdot \frac{\cos^2 a + \sin^2 a}{\cos^2 a} =[/m]
[m]= \sin a \cdot \cos a \cdot \frac{1}{\cos^2 a} = \frac{\sin a}{\cos a} = tg\ a[/m]