The Total solution for NCERT class 6-12
sec4┬аx тАУ sec2┬аx= tan4┬аx + tan2┬аx
Let us consider LHS: sec4┬аxтАУ sec2┬аx
(sec2┬аx)2┬атАУsec2┬аx
By using the formula, sec2┬а╬╕ = 1 + tan2┬а╬╕.
(1 + tan2┬аx)┬а2┬атАУ(1 + tan2┬аx)
1 + 2tan2┬аx + tan4┬аxтАУ 1 тАУ tan2┬аx
tan4┬аx + tan2┬аx
= RHS
тИ┤LHS = RHS
Hence proved.