Question

1-6

Осталось 35 минут

Народ спасайте

Answer 1

$1);frac{cos^26alpha-1}{1-sin^26alpha}-tg12alpha ctg12alpha=frac{cos^26alpha-sin^26alpha-cos^26alpha}{sin^26alpha+cos^26alpha-sin^26alpha}-1=frac{-sin^26alpha}{cos^26alpha}-1=\=frac{-sin^26alpha-cos^26alpha}{cos^26alpha}=-frac1{cos^26alpha}\\2);sin8alphacos3alpha-cos8alphasin3alpha=sin(8alpha-3alpha)=sin5alpha\\3);frac{4cos^27alpha}{sin14alpha}=frac{4cos^27alpha}{2sin7alphacos7alpha}=frac{2cos7alpha}{sin7alpha}=2ctg7alpha$

$4);frac{sin14alpha-sin10alpha}{cos3alpha-cos7alpha}=frac{2sinfrac{14alpha+10alpha}2cosfrac{14alpha-10alpha}2}{-2sinfrac{3alpha+7alpha}2sinfrac{3alpha-7alpha}2}=frac{sin2alphacos12alpha}{sin5alphasin2alpha}=frac{cos12alpha}{sin5alpha}\\5);cos^2left(fracpi2-3alpharight)-cos^2(pi+3alpha)=sin^23alpha-cos^23alpha=-(cos^23alpha-sin^23alpha)=\=-cos6alpha$