Question

Знайдіть tg(π/4 - α)
якщо sin α=0,6 і π:2‹α‹π

Answer 1

$\displaystyle\bf\\\frac{\pi }{2} < \alpha < \pi \ \ \Rightarrow \ \ Cos\alpha < 0\\\\\\Cos\alpha =-\sqrt{1-Sin^{2} \alpha } =-\sqrt{1-0,6^{2} } =-\sqrt{1-0,36} =\\\\\\=-\sqrt{0,64} =-0,8\\\\\\tg\alpha =\frac{Sin\alpha }{Cos\alpha } =\frac{0,6}{-0,8} =-0,75\\\\\\tg\Big(\frac{\pi }{4} -\alpha \Big)=\frac{tg\frac{\pi }{4} -tg\alpha }{1+tg\frac{\pi }{4} \cdot tg\alpha } =\frac{1-(-0,75)}{1+1\cdot(-0,75)} =\\\\\\=\frac{1+0,75}{1-0,75} =\frac{1,75}{0,25} =7$

$\displaystyle\bf\\Otvet \ : \ tg\Big(\frac{\pi }{4} -\alpha \Big)=7$