Question

$\frac{1 + cos \: a}{1 - cos \: a } = {(cos \: a \: + cot \: a \: ) }^{2}$
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Answer 1

Step-by-step explanation:

multiply lhs fraction numerator and denominator with (1+ cosA)

1+cosA (1+cosA)² 1+cos²A+2cosA

______ = _______ = ____________

1-cosA 1- cos²A sin²A

=1/sin²A +(cosA/sinA)² + 2*(cosA/sinA)(1/sinA)

= csc²A + cot²A + 2cotA cscA

=(cscA+cotA)²