Question

cosecA (1-cosA) (cosecA+cotA)​

Answer 1

Answer:

LHS = cosecA(1 + cosA)(cosecA - cotA)

Answer 2

1 is the required answer.

$\sf \: Answer$

$\sf\csc \:A(1 - \cos A )( \csc \:A + \cot \:A)$

Multiply cosec A with (1 - cos A)

$\sf (\csc \:A - \csc \ A \cos \:A)( \csc A \: + cot \:A)$

Note that

$\longmapsto\sf \csc A \: cos \:A = \cot \:A$

$\sf (\csc \:A - \cot\:A)( \csc A \: + cot \:A) \\ \sf{ \csc }^{2} A - {cot}^{2} A$

Remember that

$\longrightarrow \sf1 + {cot}^{2} A = cosec {}^{2} A$

Therefore ,

$\sf \: cosec {}^{2} A - cot {}^{2} = 1$

Therefore, the required answer is 1 .

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Hopefully it will help you to resolve your problem !!