Question

calcule o valor de tg (arccos 12/13)

Answer 1

arccos 12/13 = a

cos a = 12/13

cos²a+sen²a=1

144/169+sen²a=1

sen²a=1-144/169

sen²a=25/169

sena=5/13

tga = sena/cosa

tga=sena/cosa=tg(arcos 12/13) =(5/13)/(12/13)

tg (arccos 12/13)=(5/13)(13/12)

tg (arccos 12/13)=5/12

Answer 2

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$\sf arc~cos\bigg(\dfrac{12}{13}\bigg)=a\implies cos(a)=\dfrac{12}{13}\\\sf tg\bigg(arc~cos\bigg(\dfrac{12}{13}\bigg)\bigg)=tg(a)\\\sf sec(a)=\dfrac{13}{12}\\\sf tg^2(a)=\bigg(\dfrac{13}{12}\bigg)^2-1\\\sf tg^2(a)=\dfrac{169}{144}-1\\\sf tg^2(a)=\dfrac{169-144}{144}\\\sf tg^2(a)=\dfrac{25}{144}\\\sf tg(a)=\dfrac{\sqrt{25}}{\sqrt{144}}\\\sf tg(a)=\dfrac{5}{12}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf tg\bigg(arc~cos\bigg(\dfrac{12}{13}\bigg)\bigg)=\dfrac{5}{12}}}}}\blue{\checkmark}$