Question

Ilf
tan theta + (1/ tan theta) = 2,
then theta=?​

Answer 1

Answer:

45°

Step-by-step explanation:

value of tan 45° = 1

1+1/1

2

Answer 2

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$\mathsf{tan\theta = 1}$

$\boxed{\green{\mathsf{Explanation}}}$

Given

$\mathsf{tan \theta +\dfrac{1}{tan \theta} = 2}$

To Find

$\mathsf{tan \theta}$

Solution

$\mathsf{tan \theta +\dfrac{1}{tan \theta} = 2}$

$\mathsf{\dfrac{{tan}^{2} \theta + 1}{tan \theta} = 2}$

$\mathsf{{tan}^{2} \theta + 1 = 2tan\theta}$

$\mathsf{{tan}^{2} \theta - 2tan\theta +1 = 0}$

$\mathsf{{tan}^{2} \theta -tan\theta -tan \theta +1 = 0}$

$\mathsf{tan\theta (tan\theta- 1 ) -(tan\theta-1) = 0}$

$\mathsf{(tan\theta- 1)(tan\theta-1) = 0}$

$\mathsf{tan\theta = 1}$