Question

What basic trigonometric identity would you use to verify that csc x sec x cot x = csc^(2)x

Answer 1

Explanation:

Using the basic trigonometry identity, we have

`cosecx=(1)/(sinx)`,
`secx=(1)/(cosx)` and
`cotx=(cosx)/(sinx)`

Thus, the given equation is:

`{\text}{cosecx secx cotx}=cosec^2x`

Taking the LHS of the above equation , we get

=
`{\text}{cosecx secx cotx}`

=
`cosecx((1)/(cosx))((cosx)/(sinx))`

=
`cosec^2x`

=RHS

Hence proved.

Answer 2

`cotx=(cosx)/(sinx)`

`secx=(1)/(cosx)`

`cscx=(1)/(sinx)`

Explanation:

1. Keeping on mind that
`secx=(1)/(cosx)` and
`cotx=(cos)/(sin)`, you can rewrite it as following:

`cscx((1)/(cosx))((cosx)/(sinx))`

2. Then, when you simplify it, you obtain:

`cscx(1)/(sinx)`

3. So, keeping on mind that
`cscx=(1)/(sinx)`, you have:

`cscx*cscx=csc^(2)x`