Question

tan theta +tan 2 theta +tan theta. tan 2 theta = 1 solve answer urgently

Answer 1

tan3θ = tan (2θ+θ) = tan2θ + tanθ / 1- tanθtan2θ

given    tanθ +tan2θ + tanθtan2θ = 1

            tanθ + tan2θ = 1- tanθtan2θ

           tanθ + tan2θ / 1 - tanθtan2θ = 1

          tan3θ = 1   

          tan3θ = tan 45  

          3θ = 45  

            θ = 45/3  = 15  or  π/12

hope this helps.

Answer 2

Answer:

$\theta =15$

Step-by-step explanation:

To solve : $\tan\theta +\tan2\theta + \tan\theta\tan2 \theta= 1$

Solution :

We solve the expression as,

$\tan\theta +\tan2\theta + \tan\theta\tan2 \theta= 1$

$\tan\theta +\tan2\theta= 1-\tan\theta\tan 2 \theta$ ....(1)

Using identity,

$\tan 3\theta = \tan (2\theta+\theta$

$\tan 3\theta =\frac{\tan2\theta + \tan\theta}{1- \tan\theta\tan2\theta}$

Substituting (1),

$\tan 3\theta =\frac{1-\tan\theta\tan 2 \theta}{1- \tan\theta\tan2\theta}$

$\tan 3\theta =1$

$\tan 3\theta =\tan 45$

$3\theta =45$

$\theta =\frac{45}{3}$

$\theta =15$

Therefore, $\theta =15$