Proszę o pomoc! Dam naj! Zadanie potrzebę na już ! Zadanie 6. Zdjęcie w załączniku.

6a) [latex]sin alpha *tg alpha +cos alpha =sin alpha * frac{sin alpha }{cos alpha }+cos alpha = [/latex] [latex]= frac{sin^{2} alpha }{cos alpha }+ frac{cos^{2} alpha }{cos alpha } = frac{sin^{2} alpha +cos^{2} alpha }{cos alpha } = frac{1}{cos alpha } [/latex] 6b) [latex]tg^{2} alpha - frac{1}{cos^{2} alpha }= frac{sin^{2} alpha }{cos^{2} alpha }- frac{1}{cos^{2} alpha }= frac{sin^{2} alpha -1}{cos^{2} alpha }= frac{cos^{2} alpha }{cos^{2} alpha }=1 [/latex] 6c) [latex](sin alpha +cos alpha )^{2}-(sin alpha -cos alpha )^{2}= [/latex] [latex](sin^{2} alpha +2sin alpha cos alpha +cos^{2} alpha )-(sin^{2} alpha -2sin alpha cos alpha +cos^{2} alpha )= [/latex] [latex]4sin alpha cos alpha =2sin2 alpha [/latex] 6d) [latex]( frac{1}{cos^{2} alpha}-1)( frac{1}{sin^{2} alpha }-1)=( frac{1-cos^{2} alpha }{cos^{2} alpha })( frac{1-sin^{2} alpha }{sin^{2} alpha })= [/latex] [latex]= frac{sin^{2} alpha }{cos^{2} alpha } * frac{cos^{2} alpha }{sin^{2} alpha }=1 [/latex] jedynka trygonometryczna [latex]sin^{2} alpha +cos^{2} alpha =1[/latex]

Odpowiedź w załączniku.