How to do you prove this identity?
\(\tan \dfrac{\theta}{2} = \dfrac{\sin \theta}{1 + \cos \theta}\)
+23252 If you are allowed to start with the identity: tan( x/2 ) = ( 1 - cos(x) ) / sin(x) then:
tan( x/2 ) = ( 1 - cos(x) ) / sin(x) =
multiply both the numerator and denominator by ( 1 + cos(x) )
= ( 1 - cos(x) ) / sin(x) · ( 1 + cos(x) ) / ( 1 + cos(x) )
= [ ( 1 - cos(x) ) · ( 1 + cos(x) ) ] / [ sin(x) · ( 1 + cos(x) ) ]
= [ 1 - cos2(x) ] / [ sin(x) · ( 1 + cos(x) ) ]
= sin2(x) / [ sin(x) · ( 1 + cos(x) ) ]
= sin(x) / ( 1 + cos(x) )
