Question

(cosecA - cotA)^2=1-cosA/1+cosA ​

Answer 1

L.H.S (CosecA - CotA)^2

= (1/sinA - CosA/SinA)^2

= ( 1 - cosA/SinA )^2

= ( 1 - CosA)^2/ 1 - cos^2 A

= ( 1 - CosA )^2/(1)^2 - ( cos A )^2

= ( 1 - CosA )^2/ (1+CosA)(1-cosA)

= 1 - CosA/ 1+CosA R.H.S

(Proved)

Answer 2

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