Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 08
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Question 08 

Rewrite as a rational function, without any trigonometric functions. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

If is the angle in a rightangled triangle, what do you know about the sidelengths? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Suppose for a second that and draw it as the angle in a rightangled triangle. Then, up to scaling the whole triangle, the opposite side has length and the adjacent side has length 1. By Pythagoras' theorem, the hypotenuse has length . We can see then that a number that is independent of scaling. In general, if we don't assume that , then by applying the same thought process using a triangle in the 4th quadrant of the trigonometric circle, we obtain the same result: 