Question

plz answer this question immediately step by step​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

cos α = - 3/5

cos²α + sin²α = 1

9/25 + sin²α = 1

sin²α = 1 - 9/25 = 16/25

sin α = 4/ 5

$\frac{ \cosec( \alpha ) + \cot( \alpha ) }{ \sec( \alpha ) - \tan( \alpha ) } \\ = \frac{ \frac{1}{ \sin( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } }{ \frac{1}{ \cos( \alpha ) } - \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } \\ = \frac{ \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } }{ \frac{1 - \sin( \alpha ) }{ \cos( \alpha ) } } \\ = \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } \times \frac{ \cos( \alpha ) }{1 - \sin( \alpha ) } \\ = \frac{ \cos( \alpha ) + { \cos }^{2} (\alpha ) }{ \sin( \alpha ) - { \sin}^{2} ( \alpha) } \\ = \frac{( - \frac{3}{5} ) + {( - \frac{3}{5}) }^{2} }{ \frac{4}{5} - {( \frac{4}{5}) }^{2} } \\ = \frac{( - \frac{3}{5}) + \frac{9}{25} }{ \frac{4}{5} - \frac{16}{25} } \\ = \frac{( - \frac{3 \times 5}{5 \times 5}) + \frac{9}{25} }{ \frac{4 \times 5}{5 \times 5} - \frac{16}{25} } \\ = \frac{ - \frac{15}{25} + \frac{9}{25} }{ \frac{20}{25} - \frac{16}{25} } \\ = \frac{ \frac{ - 15 + 9}{25} }{ \frac{20 - 16}{25} } \\ = \frac{ - 6}{4} = \frac{ - 3}{2}$