Expert: Ahmed Salami - 7/2/2009

Question
prove following identity:  (1+tanx)/(1+cotx)=(secx)/(cscx)

Answer
Hi Zack,
First remember that;
cotx = 1/tanx
secx = 1/cosx
cscx = 1/sinx
and tanx = sinx/cosx
Now,
1 + cotx = 1 + 1/tanx
        = tanx/tanx + 1/tanx
        = (tanx + 1)/tanx
and so,
(1 + tanx)/(1 + cotx) = (1 + tanx) / [(tanx + 1)/tanx]
                     = (1 + tanx) . [tanx/(tanx + 1)]
                     = tanx
                     = sinx/cosx
                     = (1/cscx) / (1/secx)
                     = (1/cscx) . (secx/1)
                     = secx /cscx

Regards