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

3 Answers
NickTheTurtle
Apr 13, 2018

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

Explanation:

First, convert all of the trigonometric functions to sin(x) and cos(x):

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

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

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

Use the identity sin^2(x)+cos^2(x)=1:

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

Canceling out the sin^2(x) present in both the numerator and the denominator:

=1/cos^2(x)

=sec^2(x)

VYSHU
Apr 13, 2018

The answer is sec^2x.

Explanation:

We know that,
sec^2x-1=tan^2x

Therefore,(sec^2x-1)/sin^2x
=tan^2x/sin^2x
=sin^2x/cos^2x*1/sin^2x
=1/cos^2x

=sec^2x

Jim G.
Apr 13, 2018

sec^2x

Explanation:

"using the "color(blue)"trigonometric identities"

•color(white)(x)secx=1/cosx

•color(white)(x)sin^2x+cos^2x=1

rArr(1/cos^2x-cos^2x/cos^2x)/sin^2x

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

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

=cancel(sin^2x)/cos^2x xx1/cancel(sin^2x)

=1/cos^2x=sec^2x

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