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

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Answer 1 · 2016-02-10T14:47:28

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

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 · 2016-02-10T14:50:13

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

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

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

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

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