Question

(CosecA -cotA)^2=1-cosA÷1+cosA

Answer 1

Answer:

(1/sin A- cos A/sin A)2    ( 2 is in form of square.)

(1-cos A/sin A)2

(1-cos A)2/(sin A)2

sin 2 A +cos 2 A= 1

(1-cos A)(1-cos A)/1- cos 2 A

putting identity a2 - b2

(1-cos A)(1-cos A)/(1- cos A)(1 +cos A)

(1-cos A)/(1 +cos A)

hence proved.

Step-by-step explanation:

Answer 2

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