Question 903431
Express sin(x) in terms of sec(x).
<pre>
Start with this identity:

{{{sin^2(x)+cos^2(x)=1}}}

replace {{{cos(x)}}} by {{{1/(sec(x))}}}:

{{{sin^2(x)+(1/(sec(x)))^2=1}}}

{{{sin^2(x)+1/(sec^2(x))=1}}}

Multiply through by sec˛(x):

{{{sec^2(x)sin^2(x)+1=sec^2(x)}}}

Subtract 1 from both sides:

{{{sec^2(x)sin^2(x)=sec^2(x)-1}}}

Divide both sides by sec˛(x):

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

Take ± square root:

{{{sin(x)}}}{{{""=""}}}{{{""+-sqrt((sec^2(x)-1)/(sec^2(x)))}}}

Simplify:

{{{sin(x)}}}{{{""=""}}}{{{""+-sqrt(sec^2(x)-1)/(sec(x))}}}

[Which sign to take will depend on the quadrant x is in.]

Edwin</pre>