Question

How do you verify `1-cos(2x)*sec^2(x) = (tan(x))^2`?

Answer 1

LHS=`1-cos(2x)*sec^2(x)`
putting `cos2x=2cos^2x-1`
`=1-(2cos^2x-1)*sec^2(x)`
`=1-(2cos^2x*sec^2x-sec^2(x))`
`=1-2+sec^2x=sec^2x-1=tan^2x=(tanx)^2=RHS`