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anonymous
 one year ago
hey guys, need help is solving cos(2tan^1x)
anonymous
 one year ago
hey guys, need help is solving cos(2tan^1x)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do you have to do with that function...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea fair call, probs a good idea to apply what arctanx means

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\large\rm \cos(2\color{orangered}{\arctan x})\] If \(\large\rm arctan x=\theta\) then \(\large\rm \tan\theta=x\) This arctangent is just some angle.\[\large\rm \cos(2\color{orangered}{\arctan x})=\cos(2\color{orangered}{\theta})\]So we need to apply our Double Angle Formula for Cosine. It shows up in three different forms, any of them will do.\[\large\rm \cos(2\theta)=2\cos^2\theta1\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0We should draw a triangle to show what is going on with this tangent function.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\large\rm \tan \theta=x\qquad\to\qquad \tan\theta=\frac{x}{1}=\frac{opposite}{adjacent}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444291207356:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Then use Pythagorean Theorem to find the missing hypotenuse.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ye lel i'll delete mine

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0And use that information to finish it off

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0probs a good idea to realise \[\theta=\tan ^{1}x\] and you therefore wants to find \[\cos(2\theta)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then use trig identities
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