Expert: Ahmed Salami - 5/20/2009

Question
prove this trig. funtion.
(Tanx + sinx)/2tanx= cos^2(x/2)

Answer
Hi Ashley,
By the double angle formula,
cos 2A = 2cos^2 A - 1
i.e
cos^2 A = (cos 2A + 1)/2
        = (1/2)cos 2A + 1/2
let A = x/2, then
cos^2 (x/2) = (1/2)cos 2(x/2) + 1/2
           = (1/2)cosx + 1/2
Now,
(tanx + sinx)/2tanx = tanx/2tanx + sinx/2tanx
                   = 1/2 + (1/2)cosx
                   = cos^2 (x/2)

Regards