Question:
If $\cot A+\frac{1}{\cot A}=2$, find the value of $\left(\cot ^{2} A+\frac{1}{\cot ^{2} A}\right)$
Solution:
Given : $\cot A+\frac{1}{\cot A}=2$
$\cot A+\frac{1}{\cot A}=2$
Squaring both sides, we get
$\Rightarrow\left(\cot A+\frac{1}{\cot A}\right)^{2}=2^{2}$
$\Rightarrow \cot ^{2} A+\left(\frac{1}{\cot A}\right)^{2}+2(\cot A)\left(\frac{1}{\cot A}\right)=4$
$\Rightarrow \cot ^{2} A+\frac{1}{\cot ^{2} A}+2=4$
$\Rightarrow \cot ^{2} A+\frac{1}{\cot ^{2} A}=4-2$
$\Rightarrow \cot ^{2} A+\frac{1}{\cot ^{2} A}=2$
Hence, the value of $\left(\cot ^{2} A+\frac{1}{\cot ^{2} A}\right)$ is 2 .
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.