Hi,
I hope someone can help. It would be great if someone could explain how 2((secx)^4 + 2(secx)^2(tanx)^2) equals -2(cos(2x)-2)(secx)^4
I know that the expressions are related in some way, I just can't pinpoint what.
- Olivia
working on the right side to get the left ...how 2((secx)^4 + 2(secx)^2(tanx)^2) equals -2(cos(2x)-2)(secx)^4
$-2(\cos(2x)-2)\sec^4{x}$
$-2(2\cos^2{x}-1-2)\sec^4{x}$
$2(3-2\cos^2{x})\sec^4{x}$
$2(3\sec^4{x} - 2\sec^2{x})$
$2(\sec^4{x} + 2\sec^4{x} - 2\sec^2{x})$
$2[\sec^4{x} + 2\sec^2{x}( \sec^2{x} - 1)]$
$2(\sec^4{x} + 2\sec^2{x}\tan^2{x})$