Question

Докажите тождества: а) 1/sinx - cosx*ctgx=sinx; b) 1/cos(betta) - sin(betta) * tg(betta) = cos(betta)

Answer 1

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

$\frac{1}{cos\beta}-sin \beta \cdot tg\beta=\frac{1}{cos\beta}- \frac{sin \beta \cdot sin \beta}{cos \beta}=\frac{1-sin^2\beta}{cos \beta}= \frac{cos^2 \beta}{cos \beta}=cos \beta$