Question

Are the following equations or identities?

1) `tan x=sin x/cos x`

2) `secx=sinx/cosx`.

3) `cscx = 1/sinx`

4) `secx = 1/(1/sinx)`

Answer 1

1) identity
2) equation.
3) identity
4) equation.

Explanation:

1) By the definition, (basic trigonometry) we have:

`tan x=sin x/cos x`

so the first statement is an identity

2) By the definition, (basic trigonometry) we have:

`secx=1/cosx != sinx/cosx`

so the second statement is not an identity, and is therefore an equation.

3) By the definition, (basic trigonometry) we have

`cscx = 1/sinx`

so the third statement is an identity

4) By the definition, (basic trigonometry) we have

`secx = 1/cosx != 1/(1/sinx)`

so the fourth statement is not an identity, and is therefore an equation.