((cosec^2A)/(cosecA-1))-((cosec^2A)/(cosecA+1))=2 sec^2A?

1 Answer
Feb 22, 2018

For a Proof, please refer to the Explanation.

Explanation:

#csc^2A/(cscA-1)-csc^2A/(cscA+1),#

#=csc^2A{1/(cscA-1)-1/(cscA+1)},#

#=csc^2A[{(cscA+1)-(cscA-1)}/{(cscA+1)(cscA+1)}]#,

#=csc^2A{2/(csc^2A-1)}#,

#=csc^2A{2/cot^2A}.........[csc^2A=cot^2A+1}#,

#=2csc^2A*tan^2A#,

#=2csc^2A{sin^2A*1/cos^2A}#,

#={2*(csc^2A*sin^2A)}1/cos^2A#,

#=2*1*sec^2A=2sec^2A,# as desired!