How to simplify csc⁡(−x)cot⁡(−x)?

Foemicofeduz

Foemicofeduz

Answered

2023-01-01

How to simplify csc(x)cot(x)?

Answer & Explanation

Anabel Phillips

Anabel Phillips

Expert

2023-01-02Added 6 answers

csc(x)cot(x)=cscxcotx=cscxcotx=1sinxcosxsinx
=1cosx=secx
Taniyah Hartman

Taniyah Hartman

Expert

2023-01-03Added 1 answers

Let: csc(x)cot(x)
Let's apply the fact that csc(x) and cot(x) are odd functions:
=csc(x)cot(x)
=csc(x)cot(x)
Applying two common trigonometric identities will follow.; csc(x)=1sin(x) and cot(x)=cos(x)sin(x):
=1sin(x)cos(x)sin(x)
=1sin(x)sin(x)cos(x)
=1cos(x)
Finally, let's apply another standard trigonometric identity; sec(x)=1cos(x):
=sec(x)

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