Question

verify sec^4x-tan^4x=sec^2x+tan^2x

Answer 1

i will do left side first.

Answer 2

1/cos^4x-sin^4x/cos^4x= (1-sin^4x)/(cos^2x)(cos^2x)= (1+sin^2x)(1-sin^2x)/(cos^2x)(1-sin^2x)= (1+sin^2x)/cos^2x

Answer 3

Now i will do right side. 1/cos^2x+sin^2x/cos^2x=(1+sin^2x)/(cos^2x)= Left side. QED