Question

доказать тождество cosa/1+sina + cosa/1-sina= 2/cosa

Answer 1

cosa/1+sina+cosa/1-sina=cosa(1-sina)+cosa(1+sina)/1-sin²a=cosa-sin*cosa+cosa+sin*COSA/1-sin²a=2cosa/cos²a=2/cosa

Answer 2

$\L=frac{cosalpha}{1+sinalpha}+frac{cosalpha}{1-sinalpha}=frac{cosalpha(1-sinalpha)+cosalpha(1+cosalpha)}{(1+sinalpha)(1-sinalpha)}= \. \frac{cosalpha-cosalpha*sinalpha+cosalpha+cosalpha*sinalpha}{1-sin^2alpha}=frac{2cosalpha}{cos^2alpha}=frac{2}{cosalpha} \. \L=P$