Question

Prove that :
Sec^2- Cos^2 = Sin^2[Sec^2+1]

Answer 1

Answer:

sin²x[sec²+1]

Step-by-step explanation:

sec²x-cos²x

=1/cos²x - cos²x

={1-cos^4x}/cos^2x

={1+cos²x}{1-cos²x}/cos²x

=sin^2x[{1+cos²x}]/cos²x

=sin²x(sec²x+1) ( proved)