How do you simplify the expression 1-sec^2x?

1 Answer
Aug 25, 2016

-tan^2x

Explanation:

Begin from the color(blue)"basic trigonometric identity"

color(red)(|bar(ul(color(white)(a/a)color(black)(sin^2x+cos^2x=1)color(white)(a/a)|)))

divide all terms on both sides by cos^2x

rArr(sin^2x)/(cos^2x)+(cos^2x)/(cos^2x)=1/(cos^2x)

color(orange)"Reminder"

color(red)(|bar(ul(color(white)(a/a)color(black)(tanx=(sinx)/(cosx)" and " secx=1/(cosx))color(white)(a/a)|)))

Hence identity simplifies to.

tan^2x+1=sec^2xrArrtan^2x=sec^2x-1

multiply through by -1

rArr-tan^2x=1-sec^2x