Question

prove that (cosecA-cotA)^2=1-cosA/1+cosA​

Answer 1

Answer:

Given:

The equation is,

1-cosA/1+cosA=(CosecA-cotA)²

Solution:

Take LHS,

1-cosA/1+cosA

on rationalizing,

1-cosA/1+cosA×1-cosA/1-cosA

=(1-cosA)²/1-cos²A

=1+cos²A-2cosA/sin²A

=1/sin²A+cos²A/sin²A-2cosA/sinA

=cosec²A+cot²A-2cosecA.cotA

=(CosecA-cotA)²

LHS=RHS

Step-by-step explanation:

Hope it helps you.....

Answer 2

Step-by-step explanation:

$( {cosecA - cotA})^{2} \\ \\ = ( { \frac{1 - cosA}{sinA} })^{2} \\ \\ = \frac{( {1 - cosA})^{2} }{ {sin}^{2} A} \\ \\ = \frac{( {1 - cosA})^{2} }{1 - {cos}^{2}A } \\ \\ = \frac{1 - cosA}{1 + cosA}$