# `csc(-x)/sec(-x) = -cot(x)` Verfiy the identity. Verify the identity: `csc(-x)/sec(-x)=-cot(x)`

Simplify the left side of the equation using the following even/odd identities:

csc(-x)=-csc(x)  and  sec(-x)=sec(x)

`[-csc(x)]/sec(x)=-cot(x)`

`-csc(x)*1/sec(x)=-cot(x)`

Simplify the left side of the equation using the following reciprocal identities:

csc(x)=1/sin(x)  and 1/sec(x)=cos(x)

`-1/sin(x)*cos(x)=-cot(x)`

`-cos(x)/sin(x)=-cot(x)`

Simplify the left side of the equation using the quotient identity.

`-cot(x)=-cot(x)`

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Verify the identity: `csc(-x)/sec(-x)=-cot(x)`

Simplify the left side of the equation using the following even/odd identities:

csc(-x)=-csc(x)  and  sec(-x)=sec(x)

`[-csc(x)]/sec(x)=-cot(x)`

`-csc(x)*1/sec(x)=-cot(x)`

Simplify the left side of the equation using the following reciprocal identities:

csc(x)=1/sin(x)  and 1/sec(x)=cos(x)

`-1/sin(x)*cos(x)=-cot(x)`

`-cos(x)/sin(x)=-cot(x)`

Simplify the left side of the equation using the quotient identity.

`-cot(x)=-cot(x)`

Approved by eNotes Editorial Team