The identity `(1 + csc x)/sec x - cot x = cos x` has to be proved.

`(1 + csc x)/sec x - cot x`

=> `(1 + 1/sin x)/(1/cos x) - (cos x)/(sin x)`

=> `(cos x + cos x/sin x) - (cos x)/(sin x)`

=> `cos x + cos x/sin x - (cos x)/(sin x)`

=> `cos x`

**This proves that **`(1 + csc x)/sec x - cot x = cos x`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now