Question

para 0 < × < 360, a soma das soluções da equação cos × = sec × e : a ) 180 b)270 c)360 d) 540 e)630

Answer 1

$\cos(x)=\sec(x)\\\\\cos(x)=\dfrac{1}{\cos(x)}\\\\\cos^2(x)=1\\\\\cos(x)=\pm\sqrt{1}\\\\\cos(x)=\pm1\\\\\\\text{Para }\cos(x)=1\text{ tem-se:}\\\\\cos(x)=1\\\\\cos(x)=\cos(360\°)\\\\\therefore\\\\\boxed{x=360\°}\\\\\\\text{Para }\cos(x)=-1\text{ tem-se:}\\\\\cos(x)=-1\\\\\cos(x)=\cos(180\°)\\\\\therefore\\\\\boxed{x=180\°}\\\\\\360\°+180\°=\boxed{\boxed{540\°}}\\\\\\\text{Alternativa d).}$