# Solving $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$ in R

• MHB
• maxkor
In summary, to solve the equation <code>tan^2x + tan^2{2x} + cot^2{3x} = 1</code> in R, you can use the <code>uniroot</code> function to find the roots within a specified interval. This function is used to find the roots of a given equation and can be used in place of other methods such as <code>optimize</code>, <code>nlm</code>, or <code>fsolve</code>. However, it is important to consider the precision of the results and have a good understanding of the syntax and functions used in R. Other programming languages such as Python or MATLAB can also be used to solve the
maxkor
Solve in R $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$.

But without desmos etc.

Beer induced reaction follows.
maxkor said:
But without desmos etc.
Wouldst thou still attempt to solve it given that you've already had a glimpse that it doesn't have a solution or do you just want to show that it doesn't have a solution?

Show that it doesn't have a solution.

isnt it $cot^2(3\pi)=\infty$

...

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## 1. What is the first step in solving this equation?

The first step in solving this equation is to rewrite it in terms of sine and cosine using the identity $\tan^2x = \frac{\sin^2x}{\cos^2x}$ and $\cot^2x = \frac{\cos^2x}{\sin^2x}$.

## 2. Can this equation be solved algebraically?

Yes, this equation can be solved algebraically by using trigonometric identities and solving for the unknown variable.

## 3. Are there any restrictions on the values of x in this equation?

Yes, there are restrictions on the values of x since the tangent and cotangent functions are undefined at certain values. In this equation, x cannot equal any odd multiple of $\frac{\pi}{2}$ or any multiple of $\pi$.

## 4. Is there a way to check my solution?

Yes, you can check your solution by plugging it back into the original equation and verifying that it satisfies the equation.

## 5. Can this equation be solved using a graphing calculator?

Yes, this equation can be solved using a graphing calculator by graphing the left side of the equation and finding the x-intercepts, which represent the solutions.

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