Question

express cos A in terms of cot A

Answer 1

$\underline{\bold{\pink{QUESTION}}}$➡

$\bold{Express \: \: cos \: A \: \: \:in \: \: terms \: \: of \: \: cot \: A. }$

$\underline{\bold{\pink{SOLUTION}}}$➡

$\underline {\bold{We \: \: know \: \: that \: \: }} \\ \\ \bold{ 1 + tan {}^{2} A = sec {}^{2} A} \\ \\ \bold{ = > sec {}^{2}A = 1 + tan {}^{2} A} \\ \\ \bold{ = > sec \: A = \sqrt{1 +tan {}^{2} A} } \\ \\ \bold{[Here \:, \: A \: \: is \: \: acute \: ;\: so \: \: A \: \: is \: \: positive]}$

$\bold{Now,} \\ \\ \bold{sec \: A = \sqrt{1 + tan {}^{2}A} } \\ \\ \bold{ = > sec \: A \: = \sqrt{1 + \frac{1}{cot {}^{2} A } } } \: \: \: \: \: \: \: \bold{ [tan \: A \: = \frac{1}{cot \: A} ]} \\ \\ = > \bold{sec \: A = \sqrt{ \frac{cot {}^{2}A + 1 }{cot {}^{2} A} }} \\ \\ \bold{ = > sec \: A = \frac{ \sqrt{cot {}^{2}a + 1 } }{cot \: A} }$

$\bold{Again} \\ \\ \bold{ \underline{We \: \: know \: \: that \: \: }} \\ \\ \bold{cos \: A = \frac{1}{sec \: A} } \\ \\ = > \bold{cos \: A = \frac{1}{ \frac{ \sqrt{cot {}^{2} A + 1}}{cot \: A} } } \\ \\ \bold{[As \: ,\: sec \: A = \frac{ \sqrt{cot {}^{2} A + 1} }{cot \: A} }$]

$\bold{\underline{\pink{ANSWER}}}$ ➡ $\boxed{\bold{cos \: A = \frac{1}{ \frac{ \sqrt{cot {}^{2} A+ 1}}{cot \: A} } } }\:$

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Answer 2

Answer:

Step-by-step explanation: