SOLUTION: Write an algebraic expression for {{{ cot(sin^-1(x/(x+1))) }}} The answer is {{{ sqrt(2x+1) / x }}} How would I set the problem up?

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Question 1131114: Write an algebraic expression for
The answer is
How would I set the problem up?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
cot(sin^-1(x/(x+1))
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If sin(t) = x/(x+1), cos(t) = sqrt[1-(x/(x+1))^2]
= sqrt[{(x+1)^2-x^2}(x+1)^2] = sqrt[(2x+1)/(x+1)^2] = sqrt(2x+1)/(x+1)
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Ans::
cot(t) = cos(t)/sin(t) = [sqrt(2x+1)/(x+1)]/[x/(x+1)] = [sqrt(2x+1)/x]
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Cheers
Stan H.
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Answer by ikleyn(52933)   (Show Source): You can put this solution on YOUR website!
.
You are given that   = ,

and they want you calculate  .



First, calculate   =  =  =  =  = .


The last step is to calculate   =  =  =  = your answer.

Done.

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You can find many similar solved problems in the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
    - Evaluating trigonometric expressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Trigonometry: Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


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