How do you simplify cot^2x-csc^2x?

3 Answers
turksvids
Jan 3, 2018

-1

Explanation:

One of the fundamental identities is 1+cot^2(x) = csc^2(x).

Starting with your given:

cot^2(x)-csc^2(x)

Replace csc^2(x) with 1+cot^2(x):

cot^2(x)-(1+cot^2(x))

=cot^2(x)-1-cot^2(x))

=-1

Anthony R.
Jan 3, 2018

cot^2x-csc^2x=-1

Explanation:

Use the identity 1+cot^2x=csc^2x

Subtract cot^2x to both sides:

1=csc^2x-cot^2x

Rewrite as:

1=-cot^2x+csc^2x

Divde both sides by a negative (-)

-1=cot^2x-csc^2x

sjc
Jan 3, 2018

-1

Explanation:

Another way is to reduce all the functions to sine and cosines

cot^2x-csc^2x=cos^2x/sin^2x-1/sin^2x

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

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

=-1

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