Question

Помогите срочно!!!!!!! даю 20 баллов!

Answer 1

α - угол третьей четверти , значит Sinα < 0 .

$Sin\alpha =-\sqrt{1-Cos^{2} \alpha } =-\sqrt{1-\Big(-\dfrac{9}{41} \Big)^{2} } =-\sqrt{1-\dfrac{81}{1681} }=\\\\\\=-\sqrt{\dfrac{1600}{1681} }=-\dfrac{40}{41} \\\\\\tg\alpha =\dfrac{Sin\alpha }{Cos\alpha } =-\dfrac{40}{41} :\Big(-\dfrac{9}{41} \Big)=\dfrac{40}{41} \cdot\dfrac{41}{9} =\dfrac{40}{9} \\\\\\tg\Big(\alpha -\dfrac{\pi }{4} \Big)=\dfrac{tg\alpha-tg\frac{\pi }{4} }{1+tg\alpha\cdot tg\frac{\pi }{4} } =\dfrac{\frac{40}{9} -1}{1+\frac{40}{9} \cdot 1} =\dfrac{31}{9} :\dfrac{49}{9} =$

$=\dfrac{31}{9} \cdot\dfrac{9}{49} =\boxed{\dfrac{31}{49}}$