Відповідь:     98,01 .

Пояснення:

Якщо  sinβ = 0,1  , то ctg²β - cos²β = cos²β/sin²β - cos²β = cos²β( 1/sin²β -

 - 1 ) = ( 1 - sin²β )( 1/sin²β - 1 ) = ( 1 - 0,1² )( 1/0,1² - 1 ) = 0,99 * 99 = 98,01 .

[tex] \sin( \beta ) = 0.1 \\ \sin {}^{2} ( \beta ) = 0.1 {}^{2} = 0.01 \\ \sin {}^{2} ( \beta ) + \cos {}^{2} ( \beta ) = 1 \\ \cos {}^{2} ( \beta ) = 1 - \sin {}^{2} ( \beta ) = 1 - 0.01 = 0.99 \\ \cot {}^{2} ( \beta ) = \frac{ \cos {}^{2} ( \beta ) }{ \sin {}^{2} ( \beta ) } = \frac{0.99}{0.01} = 99 \\ \cot {}^{2} ( \beta ) - \cos {}^{2} ( \beta ) = 99 - 0.99 = 98.01[/tex]