[tex]\\tg\alpha=\frac{1}{17} \\\frac{sin\alpha}{cos\alpha}=\frac{1}{17} /*cos\alpha \\sin\alpha=\frac{1}{17}cos\alpha \\sin^2\alpha+cos^2\alpha=1 \\\frac{1}{289}cos^2\alpha+cos^2\alpha=1 \\\frac{290}{289}cos^2\alpha}=1 \ /:\frac{290}{289} \\cos^2\alpha=\frac{289}{290} \\cos\alpha=\frac{17}{\sqrt290}=\frac{17\sqrt{290}}{290}[/tex]
ctga = 17
cosa / sina = 17/1
17sina = cosa
sina²a + cos²a = 1
sin²a + (17sina)² = 1
sin²a + 289sin²a = 1
290sin²a = 1
sin²a = 1/290
sina = √290 / 290
cosa = 17 * √290 / 290
cosa = 17√290 / 290 ---------- odpowiedź