Question

Calcule o valor da expressão: tg 45° + sen 30° / sen 45° . Cos 45° + cos 60°

Answer 1

Explicação passo-a-passo:

Temos que:

$\bullet~~\text{tg}~45^{\circ}=1$

$\bullet~~\text{sen}~30^{\circ}=\dfrac{1}{2}$

$\bullet~~\text{sen}~45^{\circ}=\dfrac{\sqrt{2}}{2}$

$\bullet~~\text{cos}~45^{\circ}=\dfrac{\sqrt{2}}{2}$

$\bullet~~\text{cos}~60^{\circ}=\dfrac{1}{2}$

Assim:

$M=\dfrac{\text{tg}~45^{\circ}+\text{sen}~30^{\circ}}{\text{sen}~45^{\circ}\cdot\text{cos}~45^{\circ}+\text{cos}~60^{\circ}}$

$M=\dfrac{1+\frac{1}{2}}{\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{2}}{2}+\frac{1}{2}}$

$M=\dfrac{\frac{2+1}{2}}{\frac{2}{4}+\frac{1}{2}}$

$M=\dfrac{\frac{3}{2}}{\frac{1}{2}+\frac{1}{2}}$

$M=\dfrac{\frac{3}{2}}{1}$

$M=\dfrac{3}{2}$