1-sina = ctga - cosa / ctga ?
I think this is meant to be
$$1-\sin a=\frac{\cot a - \cos a}{\cot a}$$
$$\frac{\cot a - \cos a}{\cot a}=1-\frac{\cos a}{\cot a}=1-\frac{\cos a}{\cos a/\sin a}=1-\sin a$$
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1-sina = ctga - cosa / ctga ???
1 - sin a = cos a / sin a - cos a / (cos a / sin a) ???
1 - sin a = cos a / sin a - sina add sin a to both sides
1 = cos a / sin a ????
Nope.......not an identity.......