Question

prove that : (1+1/tan square A) (1+1/ cot square A)= 1/ sin square A- sin four A

Answer 1

hey mate

see the attachment

Answer 2

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

= ((tan^2 A / tan^2 A) + (1 / tan^2 A))((cot^2 A / cot^2 A) + (1 / cot^2 A)) 

= ((1+ tan^2 A) / tan^2 A)((1 + cot^2 A) / cot^2 A) 

= (sec^2 A / tan^2 A)(csc^2 A / cot^2 A) 

= ((1 / cos^2 A) / (sin^2 A / cos^2 A))((1 / sin^2 A) / (cos^2 A / sin^2 A)) 

= (1 / sin^2 A)(1 / cos^2 A) 

= 1 / ((sin^2 A)(cos^2 A)) 

= 1 / ((sin^2 A)(1 - sin^2 A)) 

= 1 / (sin^2 A - sin^4 A)

=1/(sin^2A) -1/(sin^4A)

hence proved