Mathematic Problems

192. példa

Calculate the following expression for α=30°.

{formula_1502}

\frac{4 - s i n α}{1 - s i n α} - \frac{25}{4 c o s^{2} α} + \frac{2}{1 + s i n α}

= \frac{4 - s i n 30 °}{1 - s i n 30 °} - \frac{25}{4 c o s^{2} 30 °} + \frac{2}{1 + s i n 30 °}

= \frac{4 - \frac{1}{2}}{1 - \frac{1}{2}} - \frac{25}{4 {(\frac{\sqrt{3}}{2})}^{2}} + \frac{2}{1 + \frac{1}{2}}

= \frac{\frac{8 - 1}{2}}{\frac{2 - 1}{2}} - \frac{25}{4 \frac{3}{4}} + \frac{2}{\frac{2 + 1}{2}}

= \frac{\frac{7}{2}}{\frac{1}{2}} - \frac{25}{3} + \frac{2}{\frac{3}{2}}

= \frac{7 \cdot 2}{2 \cdot 1} - \frac{25}{3} + \frac{2 \cdot 2}{3}

= 7 - \frac{25}{3} + \frac{4}{3}

= \frac{21 - 25 + 4}{3}

= 0

\frac{4 - s i n α}{1 - s i n α} - \frac{25}{4 c o s^{2} α} + \frac{2}{1 + s i n α} = 0

Matematika - Képlettár