Question

If cot theta - 1 / cot theta +1 =1-root 3 / 1+root 3. Find the acute angle

Answer 1

This attachment is required answer.

Answer 2

Answer:

θ = 60°

Step-by-step explanation:

In the question,

We have been provided an equation,

We have to calculate the value of the term,

$\frac{cot\theta-1}{cot\theta+1}=\frac{1-\sqrt{3}}{1+\sqrt{3}}$

Now, on replacing the term, cotθ, with the term,

cotθ = 1 / tanθ

Therefore,

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

Now, we can say that, on comparing both the LHS and RHS, we can see,

$\frac{1-tan\theta}{1+tan\theta}=\frac{1-\sqrt{3}}{1+\sqrt{3}}\\\frac{tan45-tan60}{tan45+tan45.tan60}=\frac{1-\sqrt{3}}{1+\sqrt{3}}$

So, from the identity of trigonometric functions, we can say that,

$tan(A-B)=\frac{tanA-tanB}{1+tanA.tanB}$

Therefore, using the same identity, we can say,

tan(45 - θ) = tan(45 - 60)

So,

θ = 60°

Therefore, the value of the angle, θ = 60°.