Question

How do you simplify the expression `(cos^2t-1)/(sin^2t-1)`?

Answer 1

`tan^2t`

Explanation:

Using the `color(blue)"trigonometric identity"`

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

`rArrsin^2t=1-cos^2trArrcos^2t-1=-sin^2t`

and `cos^2t=1-sin^2trArrsin^2t-1=-cos^2t`

`rArr(cos^2t-1)/(sin^2t-1)=(-sin^2t)/(-cos^2t)=tan^2t`