Question

Решите пожалуйста, если сможете
$\frac{ \tan(50 ) - \tan(5) - 1 }{ \tan(50) \times \tan(5) }$
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Answer 1

Решение:

$\dfrac{tg ~50^\circ-tg~5^\circ - 1}{tg~50^\circ \cdot tg~5^\circ} = \dfrac{\dfrac{sin (50^\circ -5^\circ)}{cos~50^\circ\cdot cos~5^\circ} -1}{\dfrac{sin~50^\circ\cdot sin~5^\circ}{cos~50^\circ\cdot cos~5^\circ} } = \dfrac{sin~45^\circ - cos~50^\circ\cdot cos~5^\circ}{sin~50^\circ\cdot sin~5^\circ} =\\\\ \\ =\dfrac{sin~45^\circ -0,5( cos~(50^\circ+5^\circ)+cos~(50^\circ-5^\circ))}{0.5(cos~(50^\circ-5^\circ)-cos~(50^\circ+5^\circ))} =$

$\\=\dfrac{sin~45^\circ -0.5(cos~60^\circ+cos~45^\circ)}{0.5(cos~45^\circ -cos 60^\circ)} = \dfrac{cos~45^\circ - 0.5 cos~60^\circ- 0.5 cos~45^\circ}{0.5cos~45^\circ - 0.5 cos~60^\circ} =\\\\ \\=\dfrac{0.5cos~45^\circ - 0.5 cos~60^\circ}{0.5cos~45^\circ - 0.5 cos~60^\circ} = 1$