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  • Find the minimum value of the expansion  <img alt="\left(\frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}\right)^{2n}" src="http://entrancecorner.oncodecogs.com/gif.latex?%

Find the minimum value of the expansion  \left(\frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}\right)^{2n}

Option: 1

4^{-n}


Option: 2

2^{-n}


Option: 3

2^n


Option: 4

4^n


Answers (1)

best_answer

 \left(\frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}\right)^{2n}

\begin{array}{l}{\left(\frac{\sin ^{2} \theta+\cos ^{2} \theta}{\cos \theta \cdot \sin \theta}\right)^{2n}=\left(\frac{1}{\cos \theta \sin \theta}\right)^{2n}} \\\\ {\left(\frac{2}{2 \cos \theta \sin \theta}\right)^{2n}=(2 cosec2 \theta)^{2n}} \\\\ \end{array}

2^{2n}(cosec^2 2 \theta)^n

Use the fact that minimum value of (cosec^2 2 \theta)  is 1.

So minimum value of required expression is 22n

Posted by

shivangi.bhatnagar

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