Question

sec^2 A-cosec^A = sec^2•cosec^2

Answer 1

Here it is 

Take L.H.S 

= Sec^2 A+ Cosec^ A 

=1/Cos^2 A + 1/Sin^2 A 

= (Cos^2 A+Sin^2 A)/Sin^2 A.Cos^2 A 

= 1/Sin^2 A. Cos^2 A (As Sin^2 A + Cos^2 A = 1) 


or you can write as 

= 1/Sin^2 A . 1/Cos^2 A 

which is Cosec^2 A.Sec^2 A which is same as Sec^2 ACosec^2A==>R.H.S 


Hence Proved...