Question

prove
sinD=2tan(D/2)/1+tan^2(D/2)

Answer 1

Conditions

prove

$\sin D = 2\tan (D / 2) / 1 + \tan^2 (D / 2)$

Solution

\frac {2 \tan \left(\frac {D}{2}\right)}{1 + \tan^ {2} \left(\frac {D}{2}\right)} = \frac {2 \frac {\sin \left(\frac {D}{2}\right)}{\cos \left(\frac {D}{2}\right)}}{1 + \frac {\sin^ {2} \left(\frac {D}{2}\right)}{\cos^ {2} \left(\frac {D}{2}\right)}} = \frac {2 \frac {\sin \left(\frac {D}{2}\right)}{\cos \left(\frac {D}{2}\right)} \cos^ {2} \left(\frac {D}{2}\right) + \sin^ {2} \left(\frac {D}{2}\right) + \sin^ {2} \left(\frac {D}{2}\right)} $$= \frac {2 \frac {\sin \left(\frac {D}{2}\right)}{\cos \left(\frac {D}{2}\right)} \cos^ {2} \left(\frac {D}{2}\right)}{1} = 2 \sin \left(\frac {D}{2}\right) \cos \left(\frac {D}{2}\right) = \sin (D)$$

Q.E.D.