Question

ответить правильно на всё. Заранее очень благодарна!

Answer 1

1)$\frac{sin 2\alpha }{sin\alpha } =\frac{2*sin\alpha *cos\alpha }{sin\alpha } =2*cos\alpha$

2)$\frac{sin 2\alpha }{cos ^{2}\alpha -sin ^{2}\alpha } =\frac{sin 2\alpha }{cos2\alpha } =tg2\alpha$

3)$cos2\alpha +sin^{2} \alpha =cos^{2} \alpha -sin^{2} \alpha +sin ^{2} \alpha =cos^{2} \alpha$

4)$\frac{sin(50)}{2*cos(25)} =\frac{2*sin(25)*cos(25)}{2*cos(25)} =sin(25)$

5)$\frac{cos2\alpha }{cos\alpha -sin\alpha } =\frac{cos^{2} \alpha -sin^{2} \alpha }{cos\alpha -sin\alpha } =\frac{(cos\alpha -sin\alpha )*(cos\alpha +sin\alpha )}{cos\alpha -sin\alpha} =cos\alpha +sin\alpha$

6)$1-2*sin^{2} (\frac{\alpha}{4} )=cos(2*\frac{\alpha }{4} )=cos(\frac{\alpha }{2} )$

7)$(sin(\frac{\alpha }{4} )+cos(\frac{\alpha }{4} ))*(sin(\frac{\alpha }{4} )-cos(\frac{\alpha }{4} ))=sin^{2} (\frac{\alpha }{4} )-cos^{2} (\frac{\alpha }{4} )=-(cos^{2} (\frac{\alpha }{4} )-sin^{2} (\frac{\alpha }{4} ))=-cos(2*\frac{\alpha }{4} )=-cos(\frac{\alpha }{2} )$

8)$\frac{sin\alpha *cos\alpha }{1-2*sin^{2} \alpha } =\frac{\frac{sin2\alpha }{2} }{cos2\alpha } =\frac{sin2\alpha }{2*cos2\alpha } =\frac{tg\alpha }{2}$