(1-cos²a)*(1+tg²a)=(sin²x+cos²x-cos²x)*(1+(sin²x/cos²x))=
=sin²x*((cos²x+sin²x)/cos²x)=sin²x*1/cos²x=tg²x.
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(1-cos²a)*(1+tg²a)=(sin²x+cos²x-cos²x)*(1+(sin²x/cos²x))=
=sin²x*((cos²x+sin²x)/cos²x)=sin²x*1/cos²x=tg²x.