Find Values of x

  • MHB
  • Thread starter DaalChawal
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In summary, the given statement $|tanx + cotx| = |tanx| + |cotx|$ is true for any value of $x$, except for values that are integer multiples of $\pi$ or $\frac{(2n+1)\pi}{2}$. This is because $tanx$ and $cotx$ always have the same sign, making the absolute values redundant. However, it is important to note that this is only valid for $x \neq 0$, as the statement does not hold true for $x=0$. Additionally, the Triangle Inequality states that $|a+b| \leq |a| + |b|$, which is a general rule and not equivalent
  • #1
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Q. Is $ |tanx + cotx| = |tanx| + |cotx| $ true for any $x?$ If it is true, then find the values of $x$.

My Working -->

Since $tanx$ and $cotx$ always have the same sign, so this holds true for any value of $x$.
 
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  • #2
Okay I think this should hold true for any $x$ except $n \pi$ , $\frac{(2n+1) \pi }{2}$
Am I correct?
 
  • #3
In general, $\displaystyle \begin{align*} \left| a + b \right| \not\equiv \left| a \right| + \left| b \right| \end{align*}$, rather $\displaystyle \begin{align*} \left| a + b \right| \leq \left| a \right| + \left| b \right| \end{align*}$. That's called the Triangle Inequality.
 
  • #4
DaalChawal said:
Q. Is $ |tanx + cotx| = |tanx| + |cotx| $ true for any $x?$ If it is true, then find the values of $x$.

My Working -->

Since $tanx$ and $cotx$ always have the same sign, so this holds true for any value of $x$.
You have to be a bit more careful than this, as Prove It says but you essentially have \(\displaystyle \left | y + \dfrac{1}{y} \right | = |y| + \left | \dfrac{1}{y} \right |\), which is true for \(\displaystyle y \neq 0\).

So, yes.

-Dan
 

1. How do I find the value of x in an equation?

To find the value of x in an equation, you need to isolate the variable on one side of the equation by using algebraic operations such as addition, subtraction, multiplication, and division. Once you have the variable isolated, you can solve for its value by following the order of operations.

2. What is the importance of finding the value of x?

Finding the value of x is important in mathematics and science because it allows us to solve equations and understand the relationship between different variables. It also helps us make predictions and solve real-world problems.

3. Can I use a calculator to find the value of x?

Yes, you can use a calculator to find the value of x, but it is important to understand the steps involved in solving the equation manually. Calculators can be helpful for complex equations, but they should not be relied on solely.

4. What are some common methods for finding the value of x?

Some common methods for finding the value of x include substitution, elimination, and graphing. These methods are often used in different types of equations, such as linear, quadratic, and exponential equations.

5. Can I find the value of x in a word problem?

Yes, you can find the value of x in a word problem by first identifying the variables and writing an equation that represents the problem. Then, you can use the methods mentioned above to solve for the value of x. It is important to carefully read and understand the problem before attempting to find the value of x.

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