Question

Відомо, що sin ẞ = 0,1. Знайдіть значення виразу ctg² ẞ - cos² B.

Answer 1

$\mathrm{ctg}^2\beta -\cos^2\beta =\cfrac{\cos^2 \beta }{\sin^2\beta }-\cos^2\beta =\cfrac{\cos^2\beta -\cos^2\beta \sin ^2\beta }{\sin^2\beta }=\cfrac{\cos^2\beta \left ( 1-\sin^2\beta \right )}{\sin^2\beta }=\\=\cfrac{\left ( 1-\sin^2\beta \right )\left ( 1-\sin^2\beta \right )}{\sin^2\beta }=\cfrac{\left ( 1-\sin^2\beta \right )^2}{\sin^2\beta }=\left (\cfrac{1-\sin^2\beta }{\sin \beta } \right )^2=\left ( \cfrac{1}{\sin \beta }-\sin \beta \right )^2$

$\sin \beta =\cfrac{1}{10}\Rightarrow \left ( \cfrac{1}{1/10}-\cfrac{1}{10} \right )^2=\left ( 10-\cfrac{1}{10} \right )^2=\left (\cfrac{99}{10} \right )^2=\cfrac{9801}{100}$

Answer 2

Ответ:

Пошаговое объяснение:

$cos^2\beta =1-sin^2\beta =1-0,01=0,99;\\ctg^2\beta =\frac{cos^2\beta }{sin^2\beta }=\frac{0,99}{0,01}=99;\\ctg^2\beta -cos^2\beta =99-0,99=98,01;$