Expand tan(G + T)

Question image

Understand the Problem

The question is asking to expand the expression tan(G + T). This involves using the tangent addition formula to find the expanded form of the expression.

Answer

The expanded form of $\tan(G + T)$ is $$ \tan(G + T) = \frac{\tan G + \tan T}{1 - \tan G \tan T} $$
Answer for screen readers

The expanded form of $\tan(G + T)$ is

$$ \tan(G + T) = \frac{\tan G + \tan T}{1 - \tan G \tan T} $$

Steps to Solve

  1. Identify the Tangent Addition Formula

To expand the expression $\tan(G + T)$, we use the tangent addition formula:

$$ \tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} $$

Here, we set $a = G$ and $b = T$.

  1. Apply the Formula

Substituting $G$ and $T$ into the formula gives us:

$$ \tan(G + T) = \frac{\tan G + \tan T}{1 - \tan G \tan T} $$

  1. Final Expression

So, the expanded form of $\tan(G + T)$ is:

$$ \tan(G + T) = \frac{\tan G + \tan T}{1 - \tan G \tan T} $$

The expanded form of $\tan(G + T)$ is

$$ \tan(G + T) = \frac{\tan G + \tan T}{1 - \tan G \tan T} $$

More Information

This formula is often used in trigonometry, particularly in problems involving angles and their relationships. It's the basis for many calculations in physics and engineering as well.

Tips

  • Confusing the Formula: It's important to remember that the denominator is $1 - \tan G \tan T$, not $1 + \tan G \tan T$. This is a common error.
  • Mislabeling Angles: Ensure that you clearly identify which angle corresponds to $G$ and which corresponds to $T$ to avoid errors in your solutions.
Thank you for voting!
Use Quizgecko on...
Browser
Browser