Question

даю 100 баллов! помогите пожалуйста срочно!​

Answer 1

Объяснение:

a)

$\displaystyle\\\frac{sin\alpha +tg\alpha }{1+cos\alpha }=\frac{sin\alpha +\frac{sin\alpha }{cos\alpha } }{cos\alpha +1}=\frac{sin\alpha cos\alpha +sin\alpha }{cos\alpha *(cos\alpha +1)}=\\\\=\frac{sin\alpha *(cos\alpha +1)}{cos\alpha *(cos\alpha +1)}=\frac{sin\alpha }{cos\alpha } =tg\alpha.$

b)

$\displaystyle\\sin(\frac{2\pi }{3} -\alpha )cos(\frac{\pi }{3} +\alpha )-cos(\frac{2\pi }{3}-\alpha )sin(\frac{\pi }{3} +\alpha )=sin(\frac{2\pi }{3} -\alpha -(\frac{\pi }{3} +\alpha ))=\\\\=sin(\frac{2\pi }{3} -\alpha -\frac{\pi }{3} -\alpha )=sin(\frac{\pi }{3} -2\alpha ).$

c)

$\displaystyle\\1+sin(\frac{\pi }{2} -\alpha )cos(\pi -\alpha )=1+cos\alpha *(-cos\alpha )=1-cos^2\alpha =sin^2\alpha .$