Question

Calculați:
a) E = tg(4a - b), dacă tg a = 1 supra 5, tg b = 1 supra 239​

Answer 1

Explicație pas cu pas:

$tg(4a - b) = \dfrac{tg \ 4a - tg \ b}{1 + tg \ 4a \cdot tg \ b}$

$tg \ 4a = \dfrac{4tg \ a - 4tg^{3} \ a}{1 - 6tg^{2} \ a + tg^{4} \ a} = \dfrac{ \dfrac{4}{5} - \dfrac{4}{125}}{1 - \dfrac{6}{25} + \dfrac{1}{625}} = \dfrac{ \dfrac{100 - 4}{125}}{ \dfrac{625 - 150 + 1}{625}} = \dfrac{ \dfrac{96}{125}}{ \dfrac{476}{625}} = \dfrac{96 \times 625}{476 \times 125} = \dfrac{24 \times 5}{119} = \dfrac{120}{119}$

$tg(4a - b) = \dfrac{tg \ 4a - tg \ b}{1 + tg \ 4a \cdot tg \ b} = \dfrac{ \dfrac{120}{119} - \dfrac{1}{239}}{1 + \dfrac{120}{119} \cdot \dfrac{1}{239}} = \dfrac{28561}{28561} = 1$