Question 1040747
<pre><b>
{{{1 + 1/cos(x)}}}{{{""=""}}}{{{tan^2(x)/(sec(x)-1)}}}

Work with the right side

{{{tan^2(x)/(sec(x)-1)}}}

Use the identity {{{1+tan^2(theta)}}}{{{""=""}}}{{{sec^2(theta)}}}
solved for {{{tan^2(theta)}}}{{{""=""}}}{{{sec^2(theta)-1}}}


{{{(sec^2(x)-1)/(sec(x)-1)}}}

Factor the numerator as the difference of two squares:

{{{((sec(x)-1^"")(sec(x)+1^""))/(sec(x)-1)}}}

Cancel the (sec(x)-1)'s:

{{{((cross(sec(x)-1^""))(sec(x)+1^""))/(cross(sec(x)-1^""))}}}

{{{sec(x)+1}}}

Use the identity {{{sec(theta)}}}{{{""=""}}}{{{1/cos(theta)}}}

{{{1/cos(x)+1}}}

Use the commutative property:

{{{1+1/cos(x)}}}

Edwin</pre></b>