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Cos A =7/25 .Find tan A +cot A |
| Answer» cos A\xa0{tex}=\\frac{7}{25}{/tex}\xa0We know that sin2 A + cos2 A = 1{tex}\\Rightarrow{/tex}\xa0sin2\xa0A = 1 - cos2\xa0A{tex}\\Rightarrow{/tex}\xa0sin2\xa0A = 1\xa0{tex}-\\frac{49}{625}=\\frac{576}{625}{/tex}\xa0sin A\xa0{tex}=\\sqrt{\\frac{576}{625}}=\\frac{24}{25}{/tex}Now tan A\xa0{tex}=\\frac{\\sin A}{\\cos A}=\\frac{24 / 25}{7 / 25}{/tex}{tex}=\\frac{24}{7}{/tex}and cot A\xa0{tex}=\\frac{1}{\\tan A}=\\frac{7}{24}{/tex}{tex}\\therefore{/tex}\xa0tan A + cot A\xa0{tex}=\\frac{24}{7}+\\frac{7}{24}{/tex}{tex}=\\frac{625}{168}{/tex} | |