Question

(sec⁴ A − sec² A) = ?
(a) tan⁴ A − tan² A
(b) tan² A + tan⁴ A
(c) tan² A − tan⁴ A
(d) None of these

Answer 1

(b) tan² A + tan⁴ A

$$\begin{gathered} ({\text{sec}}^{4}A-{\text{sec}}^{2}A) \\ ={\text{sec}}^{2}A({\text{sec}}^{2}A-1) \\ ={\text{sec}}^{2}A\left({\text{tan}}^{2}A\right) \\ =(1+{\text{tan}}^{2}A)\left({\text{tan}}^{2}A\right) \\ ={\text{tan}}^{2}A+{\text{tan}}^{4}A \end{gathered}$$