Question 391208
<pre><font face = "batangche" color = "indigo" size = 4><b>

The other tutor unfortunately multiplied both sides by sec(x).
That is not allowed in proving identities.  That's because you
cannot multiply both sides by anything until you have proved
that it is an equation.  You can only work with one side at time
when proving an identity.  Here is how to do it working with
only the left side, leaving the right side alone:

{{{tan(x)*expr(csc(x)/sec(x))=1}}}

Use these three identities:

1.  The quotient identity:    {{{tan(x) = sin(x)/cos(x)}}}

2.  The reciprocal identity:  {{{csc(x) = 1/sin(x)}}}

3.  The reciprocal identity:  {{{sec(x) = 1/cos(x)}}}
 
Substituting:

{{{(expr(sin(x)/cos(x)))*(expr(((1/sin(x)))/((1/cos(x)))))=1}}}

Simplify the compound fraction by inverting and multiplying

{{{(expr(sin(x)/cos(x)))*expr((1/sin(x))*(cos(x)/1))=1}}}

Cancel the {{{sin(x)}}}'s

{{{(expr(cross(sin(x))/cos(x)))*expr((1/cross(sin(x)))*(cos(x)/1))=1}}}

Cancel the {{{cos(x)}}}'s

{{{(expr(cross(sin(x))/cross(cos(x))))*expr((1/cross(sin(x)))*(cross(cos(x))/1))=1}}}

All that's left is:

        1 = 1

Edwin</pre>