Question

1)Спростіть вираз ctg²β(cos²β-1

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Answer 1

Объяснение:

${ \ctg^{2} } {\beta} \cdot( {\cos^{2}}{ \beta }- 1) = \\ = { \ctg^{2} } {\beta} \cdot\big( {\cos^{2}}{ \beta }- ({\cos^{2}}{ \beta } +{\sin^{2}}{ \beta } ) \big)= \\ = { \ctg^{2} } {\beta} \cdot\big( { - }{\sin^{2}}{ \beta } \big)= \\ = \frac{{ \cos^{2} } {\beta} }{ {\sin^{2}}{ \beta } }\cdot\big( { - }{\sin^{2}}{ \beta } \big)= \\ = \frac{{{ - } \cos^{2} } {\beta}\cdot {\sin^{2}}{ \beta } }{ {\sin^{2}}{ \beta } }= - \cos ^{2}{ \beta }$