Answer to Question #148497 in Trigonometry for Sajid

Question #148497
3cos(x-30)=cos0
1
Expert's answer
2020-12-07T09:14:49-0500

"3 \\cdot \\cos (x-30\\degree) = \\cos 0\\degree \\\\\n3 \\cdot \\cos (x-30\\degree) = 1\\\\\n \\cos (x-30\\degree) = \\frac{1}{3} \\\\\n \\cos (\\frac{\\pi}{6}-x) = \\frac{1}{3} \\\\\n\\frac{\\pi}{6}-x=\\arccos(\\frac{1}{3})+2\\pi n_1, n_1\\in Z\\ \\\\ \\frac{\\pi}{6}-x=-\\arccos(\\frac{1}{3})+2\\pi n_2, n_2\\in Z \\\\\n-x=\\arccos(\\frac{1}{3})-\\frac{\\pi}{6}+2\\pi n_1, n_1\\in Z\\ \\\\ -x=-\\arccos(\\frac{1}{3})-\\frac{\\pi}{6}+2\\pi n_2, n_2\\in Z \\\\\nx=\\frac{\\pi}{6}-\\arccos\\frac{1}{3}-2\\pi n_1, n_1\\in Z\\ \\\\ x=\\frac{\\pi}{6}+\\arccos\\frac{1}{3}-2\\pi n_2, n_2\\in Z \\\\\nAnswer:\\\\\nx=\\frac{\\pi}{6}-\\arccos\\frac{1}{3}-2\\pi n_1, n_1\\in Z\\ \\\\ x=\\frac{\\pi}{6}+\\arccos\\frac{1}{3}-2\\pi n_2, n_2\\in Z"


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