Question

If tan theta 1/tan theta=2,fin tan^2theta+1/tan^2theta

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer: The value of $\bold{\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}=2}$

Given: $\tan \theta+\frac{1}{\tan \theta}=2 \ldots(1)$

To find: $\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}$  

Solution:

We know that by formula, $(a+b)^{2}=a^{2}+b^{2}+2ab$  

Hence use the above formula to find $\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}$$\begin{array}{l}{\left(\tan \theta+\frac{1}{\tan \theta}\right)^{2}=\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}+2 \times \tan \theta \times \frac{1}{\tan \theta}} \\\\ {2^{2}=\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}+2 \times 1} \\ \\{4=\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}+2} \\\\ {\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}=4-2} \\\\ {\tan ^{2} \theta+\frac{1}{\tan ^{2} \theta}=2}\end{array}$