questões de trigonometria
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Boa tarde Gerlan!
Solução!
Exercicio 83
![5sec(x)-3tan^{2}x=1\\\\\\
5 \dfrac{1}{cos(x)}-3 \dfrac{sen^{2}(x) }{cos^{2} (x) }=1\\\\\\
\dfrac{5cos(x)}{cos^{2}(x) } -3 \dfrac{sen^{2}(x) }{cos^{2} (x) }= \dfrac{cos ^{2}(x) }{cos^{2}(x)} \\\\\\\
\dfrac{ [5cos(x)-3sen^{2}x-cos^{2}x]}{cos^{2} (x)} \\\\\\\
\dfrac{5cos(x)-3[1-cos^{2}x]-cos^{2}x}{ cos^{2}(x) } \\\\\\\
\dfrac{5cos(x)-3+3cos^{2}x-cos^{2}x }{2cos^{2}x }\\\\\\\
2cos^{2}x+5cos(x)\dfrac{-3cos^{2}x }{cos^{2}x } \\\\\\\
2cos^{2}x+5cos(x)-3=0\\\\
Uma ~~equacao~~ do ~~segundo ~~grau.
5sec(x)-3tan^{2}x=1\\\\\\
5 \dfrac{1}{cos(x)}-3 \dfrac{sen^{2}(x) }{cos^{2} (x) }=1\\\\\\
\dfrac{5cos(x)}{cos^{2}(x) } -3 \dfrac{sen^{2}(x) }{cos^{2} (x) }= \dfrac{cos ^{2}(x) }{cos^{2}(x)} \\\\\\\
\dfrac{ [5cos(x)-3sen^{2}x-cos^{2}x]}{cos^{2} (x)} \\\\\\\
\dfrac{5cos(x)-3[1-cos^{2}x]-cos^{2}x}{ cos^{2}(x) } \\\\\\\
\dfrac{5cos(x)-3+3cos^{2}x-cos^{2}x }{2cos^{2}x }\\\\\\\
2cos^{2}x+5cos(x)\dfrac{-3cos^{2}x }{cos^{2}x } \\\\\\\
2cos^{2}x+5cos(x)-3=0\\\\
Uma ~~equacao~~ do ~~segundo ~~grau.](https://tex.z-dn.net/?f=5sec%28x%29-3tan%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%0A5+%5Cdfrac%7B1%7D%7Bcos%28x%29%7D-3+%5Cdfrac%7Bsen%5E%7B2%7D%28x%29+%7D%7Bcos%5E%7B2%7D+%28x%29+%7D%3D1%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B5cos%28x%29%7D%7Bcos%5E%7B2%7D%28x%29+%7D++-3+%5Cdfrac%7Bsen%5E%7B2%7D%28x%29+%7D%7Bcos%5E%7B2%7D+%28x%29+%7D%3D+%5Cdfrac%7Bcos+%5E%7B2%7D%28x%29+%7D%7Bcos%5E%7B2%7D%28x%29%7D+%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B+%5B5cos%28x%29-3sen%5E%7B2%7Dx-cos%5E%7B2%7Dx%5D%7D%7Bcos%5E%7B2%7D+%28x%29%7D+%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B5cos%28x%29-3%5B1-cos%5E%7B2%7Dx%5D-cos%5E%7B2%7Dx%7D%7B++cos%5E%7B2%7D%28x%29+%7D+%5C%5C%5C%5C%5C%5C%5C%0A++%5Cdfrac%7B5cos%28x%29-3%2B3cos%5E%7B2%7Dx-cos%5E%7B2%7Dx+%7D%7B2cos%5E%7B2%7Dx+%7D%5C%5C%5C%5C%5C%5C%5C%0A+2cos%5E%7B2%7Dx%2B5cos%28x%29%5Cdfrac%7B-3cos%5E%7B2%7Dx+%7D%7Bcos%5E%7B2%7Dx+%7D+%5C%5C%5C%5C%5C%5C%5C%0A2cos%5E%7B2%7Dx%2B5cos%28x%29-3%3D0%5C%5C%5C%5C%0AUma+%7E%7Eequacao%7E%7E+do+%7E%7Esegundo+%7E%7Egrau.%0A+)


Exercicio 84
![sen^{2}(x)-5sen(x).cos(x)+cos^{2}(x)=3\\\\\
sen^{2}(x)+cos^{2}(x)-5sen(x).cos(x)=3\\\\\\
relacao~~fundamental\\\\\\ sen^{2}x+cos^{2}x=1\\\\\\\
1-5sen(x).cos(x)=3\\\\\\\\
identidade~~cos(x)tan(x)=sen(x)~~entao.\\\\\\\\
1-5sen(x).cos(x)=3\\\\\\
-5sen(x).cos(x)=3-1\\\\\\
-5sen(x).cos(x)=2\\\\\\
-5tan(x)cos(x).cos(x)=2\\\\\\
Tan(x)= \dfrac{sen(x)}{cos(x)} \\\\\\
-5 \frac{sen(x)}{cos(x)} .cos(x)=2\\\\\\
cos(x)[ \frac{-5sen(x).1}{cos(x)}]=2\\\\\\\
sen^{2}(x)-5sen(x).cos(x)+cos^{2}(x)=3\\\\\
sen^{2}(x)+cos^{2}(x)-5sen(x).cos(x)=3\\\\\\
relacao~~fundamental\\\\\\ sen^{2}x+cos^{2}x=1\\\\\\\
1-5sen(x).cos(x)=3\\\\\\\\
identidade~~cos(x)tan(x)=sen(x)~~entao.\\\\\\\\
1-5sen(x).cos(x)=3\\\\\\
-5sen(x).cos(x)=3-1\\\\\\
-5sen(x).cos(x)=2\\\\\\
-5tan(x)cos(x).cos(x)=2\\\\\\
Tan(x)= \dfrac{sen(x)}{cos(x)} \\\\\\
-5 \frac{sen(x)}{cos(x)} .cos(x)=2\\\\\\
cos(x)[ \frac{-5sen(x).1}{cos(x)}]=2\\\\\\\](https://tex.z-dn.net/?f=sen%5E%7B2%7D%28x%29-5sen%28x%29.cos%28x%29%2Bcos%5E%7B2%7D%28x%29%3D3%5C%5C%5C%5C%5C%0Asen%5E%7B2%7D%28x%29%2Bcos%5E%7B2%7D%28x%29-5sen%28x%29.cos%28x%29%3D3%5C%5C%5C%5C%5C%5C%0Arelacao%7E%7Efundamental%5C%5C%5C%5C%5C%5C+sen%5E%7B2%7Dx%2Bcos%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%5C%0A1-5sen%28x%29.cos%28x%29%3D3%5C%5C%5C%5C%5C%5C%5C%5C%0Aidentidade%7E%7Ecos%28x%29tan%28x%29%3Dsen%28x%29%7E%7Eentao.%5C%5C%5C%5C%5C%5C%5C%5C%0A1-5sen%28x%29.cos%28x%29%3D3%5C%5C%5C%5C%5C%5C%0A-5sen%28x%29.cos%28x%29%3D3-1%5C%5C%5C%5C%5C%5C%0A-5sen%28x%29.cos%28x%29%3D2%5C%5C%5C%5C%5C%5C%0A%0A-5tan%28x%29cos%28x%29.cos%28x%29%3D2%5C%5C%5C%5C%5C%5C%0ATan%28x%29%3D+%5Cdfrac%7Bsen%28x%29%7D%7Bcos%28x%29%7D+%5C%5C%5C%5C%5C%5C%0A-5+%5Cfrac%7Bsen%28x%29%7D%7Bcos%28x%29%7D+.cos%28x%29%3D2%5C%5C%5C%5C%5C%5C%0Acos%28x%29%5B+%5Cfrac%7B-5sen%28x%29.1%7D%7Bcos%28x%29%7D%5D%3D2%5C%5C%5C%5C%5C%5C%5C+%0A%0A%0A%0A)


Boa tarde!
Bons estudos!
Solução!
Exercicio 83
Exercicio 84
Boa tarde!
Bons estudos!
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