Question

prove that (1+1/tan²A)(1+1/cot²A)=1/(sin²A-sin⁴A​) plz ans my question

Answer 1

(1+ 1/tan^2). ( 1+ 1/cot^2)

( 1+ tan^2) cot^2 ( cot^2 +1) tan^2

( 1+ tan^2) ( 1+ tan^2) cot^2

( 1+ tan^2)^2 cot^2,

sec^4 cos^2/sin^2

sec^2 /sin^2

1/ cos^2 sin^2

1/( 1- sin^2) sin^2

1/( sin^2 - sin^4)

Answer 2

Answer:

(1+ 1/tan^2). ( 1+ 1/cot^2)

( 1+ tan^2) cot^2 ( cot^2 +1) tan^2

( 1+ tan^2) ( 1+ tan^2) cot^2

( 1+ tan^2)^2 cot^2,

sec^4 cos^2/sin^2

sec^2 /sin^2

1/ cos^2 sin^2

1/( 1- sin^2) sin^2

1/( sin^2 - sin^4)