Question

Упростите:

1)sin 2β/sin²β=

2)sin 2α/2sin α - cos α=

3)0,5 tg α sin 2α+cos² α=

дробью писать 1 и 2!

 

Answer 1

$displaystyle 1)~frac{sin2beta}{sin^2beta}=frac{2sinbeta cos beta}{sin^2beta}=frac{2cosbeta}{sin beta}=2{rm ctg}beta\ \ \ 2)~ frac{sin2alpha}{2sinalpha}-cosalpha=frac{2sinalphacosalpha}{2sinalpha}-cosalpha=cosalpha-cosalpha=0\ \ \ 3)~0.5{rm tg}alphasin2alpha+cos^2alpha=0.5cdotfrac{sinalpha}{cosalpha}cdot 2sinalphacosalpha+cos^2alpha=sin^2alpha+cos^2alpha=1$