Resposta :
Lembre-se:
[tex]sen^{2} \alpha +cos^{2} \alpha =1[/tex]
[tex]tg \alpha =sen \alpha /cos \alpha [/tex]
[tex]sec \alpha =1/cos \alpha [/tex]
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[tex]sen \alpha *tg\alpha+ cos \alpha = sec \alpha [/tex]
[tex]sen \alpha * (sen \alpha /cos \alpha ) + cos \alpha = sec \alpha [/tex]
[tex](sen^{2} \alpha /cos \alpha ) + cos \alpha = sec \alpha [/tex]
[tex](sen^{2} \alpha /cos \alpha ) + (cos \alpha *cos \alpha /cos \alpha ) = sec \alpha [/tex]
[tex](sen^{2} \alpha /cos \alpha ) + (cos^{2} \alpha /cos \alpha ) = sec \alpha [/tex]
[tex](sen^{2} \alpha +cos^{2} \alpha )/cos \alpha = sec \alpha [/tex]
[tex]1/cos \alpha = sec \alpha [/tex]
[tex]sec \alpha =sec \alpha [/tex]
[tex]sen^{2} \alpha +cos^{2} \alpha =1[/tex]
[tex]tg \alpha =sen \alpha /cos \alpha [/tex]
[tex]sec \alpha =1/cos \alpha [/tex]
___________________________
[tex]sen \alpha *tg\alpha+ cos \alpha = sec \alpha [/tex]
[tex]sen \alpha * (sen \alpha /cos \alpha ) + cos \alpha = sec \alpha [/tex]
[tex](sen^{2} \alpha /cos \alpha ) + cos \alpha = sec \alpha [/tex]
[tex](sen^{2} \alpha /cos \alpha ) + (cos \alpha *cos \alpha /cos \alpha ) = sec \alpha [/tex]
[tex](sen^{2} \alpha /cos \alpha ) + (cos^{2} \alpha /cos \alpha ) = sec \alpha [/tex]
[tex](sen^{2} \alpha +cos^{2} \alpha )/cos \alpha = sec \alpha [/tex]
[tex]1/cos \alpha = sec \alpha [/tex]
[tex]sec \alpha =sec \alpha [/tex]