How do you verify the identity $sec(u/2)=+-sqrt((2tanu)/(tanu+sinu))$ ?

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Answer 1 · 2017-02-18T05:36:10

Square both sides of the equation
$(2tan u)/(tan u + sin u) = sec^2 (u/2)$
Develop the left side:
$LS = ((2sinu)/(cos u))/(sin u/(cos u) + sin u) =$

$= (2sin u)/(sin u + sin u.cos u) = (2sin u)/((sin u)(1 + cos u))$

Replace $( 1 + cos u)$ by $2cos^2 (u/2)$ , we get:

$LS = 1/cos^2 (u/2) = sec^2 (u/2)$

How do you verify the identity sec(u/2)=+-sqrt((2tanu)/(tanu+sinu))sec(u/2)=+-sqrt((2tanu)/(tanu+sinu))?