Question 39168
<pre><font size = 5><b>Prove the identity
<font color = "indigo">
sin(w)·tan w + cos(w)        =      sec(w)

<font color = "indigo">Simplify the more complicated side, the left
Use the identity tan<font face = "symbol">q</font> = sin<font face = "symbol">q</font>/cos<font face = "symbol">q</font>

Replace tan(w) by sin(w)/cos(w)</font>

       sin(w)
sin(w)·—————— + cos(w)        =      sec(w)
       cos(w)


       sin²(w)  cos(w)   
      ——————— + ———————        =      sec(w)
       cos(w)     1

<font color = "indigo">Get the LCD = cos(w)</font>


sin²(w)   cos(w)·cos(w)   
——————— + —————————————        =      sec(w)
cos(w)       1·cos(w)

sin²(w)      cos²(w)   
——————— + —————————————        =      sec(w)
cos(w)       cos(w)

<font color = "indigo">Write over the LCD</font"> 

sin²(w) +  cos²(w)   
——————————————————             =      sec(w)
     cos(w)  

<font color = "indigo">Use identity sin²<font face = "symbol">q</font> + cos²<font face = "symbol">q</font> = 1</font>

       1   
    ———————                    =      sec(w)
     cos(w)    


<font color = "indigo">Use identity sec<font face = "symbol">q</font> = 1/cos<font face = "symbol">q</font></font>

       sec(w)                  =      sec(w)

QED
<font color = "indigo">
Edwin
AnlytcPhil@aol.com</pre></font></font>