Question

if 3theta is an acute angle and tan 3theta -√3 = 0, find the value of theta
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Answer 1

Answer:

θ = 20°

Step-by-step explanation:

tan(3θ) - √3 = 0

⇒tan(3θ) = √3

As tan(60°) = √3

∴ 3θ = 60°

∴ θ = 20°

Thanks !

Answer 2

The value of θ is 20°.

Given:

3θ is acute angle.

tan(3θ) - √3 = 0

To find:

We have to find the value of θ.

Solution:

According to the question,

We have ,

tan3θ - √3 =0

⇒tan3θ =√3  --------(1)

⇒tan60°= √3          (3θ is an acute angle as given in the question)

If we replace the √3 with tan60° in the equation(1) then,

⇒tan3θ = tan60°

Now using the identity formula ,

⇒3θ - 60° = nπ      (if tana = tanb ,then a - b = nπ,n is an integer)

As given in the question, 3θ is an acute angle which means ,

n can be 0 or 1.

Now putting the values of n,

If n = 0, then

3θ - 60° = 0

⇒3θ = 60°

⇒ θ = 20°

If n = 1,

3θ - 60° = π

⇒3θ = π + 60°.

But π + 60° > 90°, and if its greater 90° then 3θ can't be a acute angle

So, θ = 20°.

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