Question

(cosecA-cotA)^2=1+cosA/1-cosA​

Answer 1

Answer:

Taking L.H.S.

> (cosecA-cotA) ^2

>. cosec^2A - 2cosecAcotA + cot^2A

>. 1/sin^2A -2×1/sinA×cosA/sinA + cos^2A/sin^2A

>. 1-2cosA+cos^2A/ sin^2A

>. (1 - cosA)^2/sin^2A

>. (1 - cosA)×(1 - cosA) /1 - cos^2A

>. (1 - cosA)×(1 - cosA) /1^2 - cos^2A

>. (1 - cosA)×(1 - cosA) /(1 - cosA)×(1 + cosA)

>. 1-cosA/1+cosA

Answer 2

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