Can someone prove this

[Chris59]

I can verify that it's true, but I don't understand the last step algebraically. Thanks

 

[pka]

View attachment 14861 I can verify that it's true, but I don't understand the last step algebraically.

Frankly, I don't understand your doubt.
\(\displaystyle \frac{1}{\tan(x)}=\cot(x)\)

 

[Steven G]

You have to know that people solve equations differently so the last step is different for different people. Can you show us your work so we can see your last step.

 

[Chris59]

To my mind it's fairly boiler plate to that point

You have to know that people solve equations differently so the last step is different for different people. Can you show us your work so we can see your last step.

 

[Steven G]

No, x = two things both in terms of y. If you knew y, then you are basically done. So solve for y using the two equations that have y. You may be surprised at what y can be but it is what it is.

 

[Dr.Peterson]

View attachment 14861 I can verify that it's true, but I don't understand the last step algebraically. Thanks

I wonder if people are misunderstanding your question, because you omitted the context.

I think that what you showed us here is part of a solution you were given, and you are asking why they wrote the last bit, which is in blue. Am I right that "the last step" refers to the blue part?

If so, then post #2 answers it. The reciprocal identify says that [MATH]\cot(x) = \frac{1}{\tan(x)}[/MATH]. Consequently,

[MATH]\frac{y}{\tan(27.2)} = y\cdot \frac{1}{\tan(27.2)} = y\cdot \cot(27.2)[/MATH],​

as they say.

If that's not what you mean, please ask your question a different way, in case we're all being dense.

 

[Chris59]

I wonder if people are misunderstanding your question, because you omitted the context.

I think that what you showed us here is part of a solution you were given, and you are asking why they wrote the last bit, which is in blue. Am I right that "the last step" refers to the blue part?

If so, then post #2 answers it. The reciprocal identify says that [MATH]\cot(x) = \frac{1}{\tan(x)}[/MATH]. Consequently,

[MATH]\frac{y}{\tan(27.2)} = y\cdot \frac{1}{\tan(27.2)} = y\cdot \cot(27.2)[/MATH],​

as they say.

If that's not what you mean, please ask your question a different way, in case we're all being dense.

Here is the entire problem in question. I understand every other aspect of it. I also am aware of the Trigonmetric identity cotangent = 1/tangent, but that's not what's stated in the line "solving Equation (1)." Replacing y with a constant yields an equality, but I just don't know how. Thanks for your help guys.

 

[Chris59]

I think you've explained this to me Dr. Thank you so much!