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

1 Answer
Jim G.
Jul 7, 2016

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

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