Question

How do you simplify `(sec^2 theta - 1 )/ sec^2 theta`?

Answer 1

`sin^2theta`

Explanation:

`color(orange)"Reminders"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(1/sectheta=costheta)color(white)(a/a)|)))`

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

Divide the terms on the numerator by `sec^2theta`

`rArr(sec^theta-1)/(sec^2theta)=sec^2theta/sec^2theta-1/sec^2theta`

and 'simplifying' : `1-cos^2theta=sin^2theta`