lgg23
  • lgg23
Calculus: tan (2 arc cos (x/3)) = ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
What are you supposed to do? Integrate, derive, solve for x...?
lgg23
  • lgg23
it says to simplify the expression
asnaseer
  • asnaseer
Since we know arccos(x/3) gives us an angle \(\alpha\) whose cosine is x/3, we can draw the following triangle and use Pytharogus to calculate the length of the third side: |dw:1328486495106:dw| From this we get:\[\tan(\alpha)=\frac{\sqrt{9-x^2}}{x}\tag{a}\]Now just use the formula for \(\tan(2\alpha)\) to get:\[\tan(2\alpha)=\frac{2\tan(\alpha)}{1-\tan^2(\alpha)}\tag{b}\]Substitute equation (a) into equation (b) and simplify.

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lgg23
  • lgg23
Thank you.
asnaseer
  • asnaseer
yw

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