Question 732932
<pre>
sin(x)tan(x) + cos(x) = sec(x)

Use the identity {{{tan(theta)=sin(theta)/cos(theta)}}}

sin(x)·{{{sin(x)/cos(x)}}} + cos(x) 

Write the sin(x) as a fraction by putting 1 under it:

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

Multiply the fractions 

{{{sin^2(x)/cos(x)}}} + cos(x)

Get an LCD of cos(x)

{{{sin^2(x)/cos(x)}}} + cos(x)·{{{cos(x)/cos(x)}}}

Write the cos(x) as a fraction by putting 1 under it:

{{{sin^2(x)/cos(x)}}} + {{{cos(x)/1}}}·{{{cos(x)/cos(x)}}}

 Multiply the fractions

{{{sin^2(x)/cos(x)}}} + {{{cos^2(x)/cos(x)}}}

Combine the numerators over the LCD:

{{{(sin^2(x)+cos^2(x))/cos(x)}}}

Use the identity {{{sin^2(theta)+cos^2(theta)=1}}}

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

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

sec(x)

Edwin</pre>