1)вычислите cos2a*tg 4a,если sin a-cos a=1/корень из 2 2)упростить ctg a + (sin a/ 1+cos...

1) $\sin a-\cos a=\frac{1}{\sqrt{2}}\\ \frac{1}{2}=(\sin a-\cos a)^2=\sin^2 a - 2\sin a \cos a + \cos^2 a = 1 - \sin 2a\\ \sin 2a = \frac{1}{2}\\ \cos 2a \tan 4a = \frac{\cos 2a \sin 4 a}{\cos 4a} = \frac{2 \cos 2a \sin 2 a \cos 2a}{1- 2\sin^2 2a}=\\ =\frac{2\sin 2a (1-\sin^2 2a)}{1-2\sin^2 a} = \frac{3}{2} = 1.5$

$\cot a + \frac{\sin a}{1+\cos a}=\frac{\cos a}{\sin a} + \frac{\sin a(1-\cos a)}{1-cos^2 a}=\\ =\frac{\cos a}{\sin a}+\frac{1-\cos a}{\sin a}=\frac{1}{\sin a}$

$\cos^2a-\cos^4a+\sin^4a = \cos^2a- ((\cos^2 a)^2 - (\sin^2 a)^2)=\\ =\cos^2 a - (\cos^2 a - \sin^2 a)(\cos^2 a + \sin^2 a) = \sin^2 a$