Question

queria ajuda sobre qual e o valor de secante de 855  graus+ cossecante de 495- cotangente de (-225 graus) 

Answer 1

$sec(855^o)+cossec(495^o)-cotg(-225^o)=\\ \\ -\sqrt2+\sqrt2-(-1)=1$

Answer 2

$\text{secante}~855^{\circ}=\dfrac{1}{\text{cos}~855^{\circ}}$.

Veja que, $855=360\times2+135$.

E $180-135=45$.

Deste modo, $\text{cos}~855^{\circ}=\text{cos}~135^{\circ}=-\text{cos}~45^{\circ}$.

Com isso, $\text{cos}~855^{\circ}=\dfrac{-\sqrt{2}}{2}$.

Assim, $\text{secante}~855^{\circ}=-\dfrac{2}{\sqrt{2}}=\dfrac{2\sqrt{2}}{2}=-\sqrt{2}$

Do mesmo modo,

$\text{cossecante}~495^{\circ}=\dfrac{1}{\text{sen}~495^{\circ}}$.

Note que, $495=360+135$.

Assim, $\text{sen}~495^{\circ}=\text{sen}~135^{\circ}$.

Como $180-135=45$, temos $\text{sen}~135^{\circ}=\text{sen}~45^{\circ}$.

Deste modo, $\text{sen}~135^{\circ}=\dfrac{\sqrt{2}}{2}$.

Com isso, $\text{cossecante}~495^{\circ}=\dfrac{2}{\sqrt{2}}=\sqrt{2}$.

Por fim, $\text{cotangente}~-225^{\circ}=-1$.

Logo:

$\text{secante}~855^{\circ}+\text{cossecante}~495^{\circ}-\text{cotangente}~-225^{\circ}=-\sqrt{2}+\sqrt{2}-(-1)=1$