Answer to Question #156106 in Trigonometry for .

Question #156106

given sin α = 3/5 and cos β = -4/5 , α is an acute angle and β is an obtuse angle find ;

a) cot α + cosec β

b) sin 2α tan 2β


1
Expert's answer
2021-01-19T03:45:35-0500

a) "\\cot{\\alpha} +\\frac{1}{\\sin{\\beta}}=\\sqrt{\\frac{1}{\\sin^2{\\alpha}}-1}+\\frac{1}{\\sqrt{1-\\cos^2{\\beta}}}=" "\\sqrt{\\frac{25}{9}-1}+\\frac{1}{\\sqrt{1-\\frac{16}{25}}}=\\frac{4}{3}+\\frac{5}{3}=3"

b)"\\sin{2\\alpha}\\tan{2\\beta}=2\\sin{\\alpha}\\cos{\\alpha}\\times \\frac{2\\sin{\\beta}\\cos{\\beta}}{\\cos^2{\\beta}-\\sin^2{\\beta}}=" "2\\sin{\\alpha}\\sqrt{1-\\sin^2{\\alpha}}\\times \\frac{2\\cos{\\beta}\\sqrt{1-\\cos^2{\\beta}}}{\\cos^2{\\beta}-1+\\cos^2{\\beta}}=" "\\frac{6}{5}\\sqrt{1-\\frac{9}{25}}\\times \\frac{-\\frac{8}{5}\\sqrt{1-\\frac{16}{25}}}{\\frac{32}{25}-1}=\\frac{24}{25}\\times(-\\frac{24}{7})=-\\frac{576}{175}"


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