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PLEASE HELP W PRECALC QUESTION

PLEASE HELP W PRECALC QUESTION-example-1
User Adris
by
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1 Answer

6 votes

Answer:
2tan(theta)

Explanation:

I know this is pre-calculus, but I want to let you know what this is actually used for in real calculus. This is a method of integration called "u-substitution" which tranforms the function of 'x' into a function of 'theta'. If we allow the value of 'x' to equal 2sec(theta), we can plug this into the function to get:


√(x^2-4) =√((2sec(theta)^2-4) =√(4sec^2(theta)-4)

Factor out a 4 to get:


√(4(sec^2(theta)-1))

Take the square root of 4 to get a 2 on the outside of the radical:


√(4(sec^2(theta)-1))=2√(sec^2(theta)-1)

Use the trig identity below to convert the secant to tangent:


tan^2(theta)+1=sec^2(theta)


tan^2(theta)=sec^2(theta)-1

Therefore our expression becomes:


2√(sec^2(theta)-1)=2√(tan^2(theta))

The square root of tangent is simply tangent:


2√(tan^2(theta)) =2tan(theta)

User Verhelst
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