Science:Math Exam Resources/Courses/MATH105/April 2016/Question 01 (k)
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Question 01 (k) 

Evaluate . Your answer must be in terms of , but it is acceptable to leave in inverse 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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Consider the trigonometric substitution. 
Hint 2 

Double angle formula 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Let . We then use the doubleangle formulas and the fact that to get
Now, we should find , and in terms of : We know that , so Also, we get . Thus,
Therefore, the final answer is:
