How do you simplify the expression 1-sec^2x?
1 Answer
Aug 25, 2016
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