Question

सिद्ध करा: sec⁴ A (1 - sin⁴ A) - 2 tan² A = 1

Answer 1

$\Large \textit{\underline{\underline{Proof...}}}$

$\displaystyle \large \textit{LHS...} \\ \\ \Rightarrow\ \sec^4 A(1-\sin^4 A)-2\tan^2A \\ \\ \Rightarrow\ \sec^4 A(1^2-(\sin^2 A)^2)-2\tan^2A \\ \\ \Rightarrow\ \sec^4A(1-\sin^2A)(1+\sin^2A)-2\tan^2A \\ \\ \Rightarrow\ \sec^4A \cdot \cos^2A(1+\sin^2A)-2\tan^2A \\ \\ \Rightarrow\ \sec^2A(1+\sin^2A)-2\tan^2A \\ \\ \Rightarrow\ \sec^2A+\sec^2A \cdot \sin^2A -2\tan^2A \\ \\ \Rightarrow\ \sec^2A+\tan^2A-2\tan^2A \\ \\ \Rightarrow\ \sec^2A-\tan^2A \\ \\ \Rightarrow\ 1 \\ \\ \Rightarrow\ \large \textit{...RHS}$

$\huge \textsc{Hence proved!!!}$