Question

If cot theta+1/cot theta=2 then find the value of cot^2theta+1/cot^2 theta

Answer 1

$\cot\theta + \frac{1}{ \cot\theta} = 2 \\ {( \cot\theta + \frac{1}{ \cot\theta})}^{2} = {2}^{2} \\ { \cot}^{2} \theta + 2 + \frac{1}{{ \cot}^{2} \theta } = 4 \\ { \cot}^{2} \theta + \frac{1}{{ \cot}^{2} \theta } =4 - 2 = 2$

Answer 2

Answer:

The required value of $cot^{2}$θ$+\frac{1}{cot^{2} }$θ $=2$

Step-by-step explanation:

Concept:

The ratio of the opposite side's length to the adjacent side's length is known as the right-angled triangle's cot theta. It also has the same value as the proportion between the angle's sine and cosine.

Given:

$cot$θ$+\frac{1}{cot}$θ $=2$

To find:

The objective is to find out the value of $cot^{2}$θ$+\frac{1}{cot^{2} }$θ

Solution:

(cotθ$+\frac{1}{cot}$θ$)^{2} =cot^{2}$θ$+\frac{1}{cot^{2} }$θ$+2cot$θ×$\frac{1}{cot}$θ

⇒$2^{2} =cot^{2}$θ+$\frac{1}{cot^{2} }$θ$+2$

⇒$cot^{2}$θ$+\frac{1}{cot^{2} }$θ $=2$

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