Question

If tan theta =1/2, then find the value of 2 cot square theta+2.

Answer 1

tan theta equals to 1 by 2 so one by cot theta equals to 1 by 2 2 cos theta equals to 2 that we will take equation 1 so we have to find the value of 2 cot square theta + 2 so from one we will put the value and get the answer

Answer 2

2cot²θ + 2 = 10

Given :

tanθ = 1/2

To find :

The value of 2cot²θ + 2

Solution :

Step 1 of 2 :

Find the value of cotθ

$\displaystyle \sf tan \theta = \frac{1}{2}$

$\displaystyle \sf{ \implies }cot \theta = \frac{1}{tan \theta}$

$\displaystyle \sf{ \implies }cot \theta = \frac{1}{ \frac{1}{2} }$

$\displaystyle \sf{ \implies }cot \theta = 2$

Step 2 of 2 :

Find the value of 2cot²θ + 2

$\displaystyle \sf{ }2{cot }^{2} \theta + 2$

$\displaystyle \sf{ } = 2 \times {2 }^{2} + 2$

$\displaystyle \sf{ } = 8 + 2$

$= 10$

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