Question

докажите тождества:

а) 1/sinx - cosx*ctgx=sinx;

b) 1/cos(betta) - sin(betta) * tg(betta) = cos(betta)

Answer 1

1) $frac{1}{sin x}-cos x cdot ctg x=frac{1}{sin x}- frac{cos x cdot cos x}{sinx}=frac{1-cos^2x}{sinx}=frac{sin^2x}{sinx}=sinx$

 

$frac{1}{cosbeta}-sin beta cdot tgbeta=frac{1}{cosbeta}- frac{sin beta cdot sin beta}{cos beta}=frac{1-sin^2beta}{cos beta}= frac{cos^2 beta}{cos beta}=cos beta$