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

3 Answers
Nghi N. ยท Nathan L.
Nov 2, 2015

Simplify (sec^2 - 1)/sec^2

Ans: sin^2 x

Explanation:

Replace sec^2 = 1/(cos^2 x into the expression , we get:
(1/(cos^2 x - 1))/(1/(cos^2 x)) = ((1 - cos^2 x)/cos^2 x)((cos^2 x)/1) =

Since (1 - cos^2 x) = sin^2x, therefore:

(sec^2 x - 1)/sec^2 x = sin^2 x

Tony B
Nov 2, 2015

sin^2x

Explanation:

1 + tan^2x=sec^2x

so " "sec^2x-1 = tan^2x

Giving " " (tan^2x)/(sec^2x)

But " "sec^2x = 1/(cos^2x)

Giving " " (tan^2x)(cos^2x)

But tan^2x =(sin^2x)/(cos^2x)

Giving " " (sin^2x) (cos^2x)/(cos^2x) = sin^2x

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Clarification: By Tony B

Given:" " (sec^2x-1)/sec^2x

But Sec^2x = 1 +tan^2x

Giving:" "(1+tan^2x-1)/(sec^2x)" "=" " tan^2x/sec^2x

But " "tanx=sinx/cosx" and "secx= 1/cosx

" "sin^2x/(cancel(cos^2x)) xxcancel(cos^2x)" "=" "sin^2x

P dilip_k
Mar 5, 2016

=sin^2x

Explanation:

(sec^2x-1)/sec^2x
=cancel(sec^2x)/cancel(sec^2x)-1/sec^2x
=1-cos^2x
=sin^2x

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