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Bonsoir , voila , j'ai un probleme pour demontrer que tg²43°- sin²43° / cotg47° + cos47° = tg43° - cos47° si vous pouvez m'eclairer plzzzzzzzzz

Sagot :

(tg²43°- sin²43°) / (cotg47° + cos47°)
=(sin(43°)/cos(43°)-sin(43°))/(cos(47°)/sin(47°)+cos(47°))
=(sin(43°)/cos(43°)-sin(43°))/(sin(43°)/cos(43°)+sin(43°))
=(sin(43°)-sin(43°)*cos(43°))/(sin(43°)+sin(43°)*cos(43°))
=(1-cos(43°))/(1+cos(43°))
=(1-cos(43°))²/(1-cos²(43°))
=(1-2cos(43°)+cos²(43°))/sin²(43°)
=sin(86°)/sin²(43°)+cos²(43°)/sin²(43°)
=sin(43°)/cos(43°)-sin(43°)
=tg(43°)-sin(43°)
= tg(43°) - cos(47°)

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