Question

How do you verify `sinx/cosx + cosx/sinx = 1`?

Answer 1

You can't verify it since it is not an identity.

Explanation:

You can't since this is not true.

To prove that this is not an identity, find one `x` for which this equation is not true.

For example, you can take `x = pi/3`:

As you know, `sin(pi/3) = sqrt(3)/2` and `cos(pi/3) = 1/2`.

`sin(pi/3) / cos(pi/3) + cos(pi/3)/sin(pi/3) = (sqrt(3)/2)/(1/2) + (1/2)/(sqrt(3)/2) = sqrt(3)/1 + 1 / sqrt(3) = 4 / sqrt(3) != 1`

Thus, this equation is not an identity.

Answer 2

The given equation is not true
and therefore can not be verified.

Explanation:

`(sin x)/(cos x)+(cos x)/(sin x)=1/(sin(x)*cos(x))!=1`

As an obvious counter-example
if `x=pi/4`
`color(white)("XXX")sin(pi/4)=cos(pi/4)`

`rArr (sin(pi/4))/(cos(pi/4))+(cos(pi/4))/(sin(pi/4))= 1+1 = 2 != 1`