Question

sec^2o-cos^2O = sin^2 (sec^2 0 + 1)​

Answer 1

To Prove :

sec²∅ - cos²∅ = tan(sec²∅ + 1)

LHS :

sec²∅ - cos²∅

→ sec²∅ - 1/sec²∅

→ (sec⁴∅ - 1)/sec²∅

→ [(sec²∅ + 1)(sec²∅ - 1)]/sec²∅

→ [(sec²∅ + 1)(1 - cos²∅)]/sec²∅

→ (sec²∅ + 1) × tan²∅/sec²∅

→ sin²∅(1 + sec²∅) → RHS

Hence, Proved

Answer 2

☆Refer to the attachment please