Question

$if \: \cot \: a + \frac{1}{ \cot \: a } = 2. \: find \: the \: value \: of \: ( \cot {}^{2} a + \frac{1}{ \cot {}^{2} a } )$
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Answer 1

Given,

$\rm \: cot \: a + \frac{1}{cot \: a} = 2$

we have to find :

$\rm {cot}^{2} \: a + \frac{1}{ {cot}^{2} \: a}$

Solution :

we know that,

${x}^{2} + {y}^{2} = (x + y) {}^{2} - 2xy$

Now,

${ \boxed{\boxed{\begin{array}{cc} \small{ \rm \: {cot}^{2} \: a + \frac{1}{ {cot}^{2} \: a } = {(cot}^{} \: a + \frac{1}{cot \:a} \:) {}^{2} - 2 \times cot \: a \times \frac{1}{cot \: a} }\\ \\ \rm = {2}^{2} - 2 \\ \\ = 4 - 2 \\ \\ = 2 \\ \\ \therefore \: \rm \: {cot}^{2} \: a + \frac{1}{ {cot}^{2} \: a } = 2\end{array}}}}$