The Total solution for NCERT class 6-12
sec4 x – sec2 x= tan4 x + tan2 x
Let us consider LHS: sec4 x– sec2 x
(sec2 x)2 –sec2 x
By using the formula, sec2 θ = 1 + tan2 θ.
(1 + tan2 x) 2 –(1 + tan2 x)
1 + 2tan2 x + tan4 x– 1 – tan2 x
tan4 x + tan2 x
= RHS
∴LHS = RHS
Hence proved.