Question

sec square theta - cos square theta =sin square ( sec square+1)

Answer 1

Here,
Sec²∅ - Cos²∅ = Sin² ∅( Sec²∅ + 1 )



= Sec²∅ - Cos²∅


= 1 / Cos²∅ - Cos²∅


= 1 - Cos⁴∅ / Cos²∅


= ( 1 - Cos²∅ ) ( 1 + Cos²∅ ) / Cos²∅


= Sin² ∅ ( 1 + Cos²∅ ) / Cos²∅


= Sin²∅ ( 1 / Cos²∅ + Cos²0 / Cos²∅ )


= Sin²∅ ( sec²∅ + 1 )


Hence Proved
Hope you understand