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anonymous
 5 years ago
the value of tan(2tan^1 (1/5)pi/4) is?
anonymous
 5 years ago
the value of tan(2tan^1 (1/5)pi/4) is?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let\[\theta=2\tan^{1} (1/5)(\pi/4)\]Form a triangle with tan theta

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let x= \[\tan^{1} \frac{1}{5}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so our expression becomes \[\tan(2x\frac{\pi}{4})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now apply difference of angle formula

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\tan(AB) = \frac{\tan(A)\tan(B) } {1+\tan(A)\tan(B) } \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\tan(2x) 1}{1+\tan(2x)} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but ,\[\tan(2x) = \frac{\sin(2x)}{\cos(2x)} = \frac{2\sin(x)\cos(x)}{\cos^2(x)\sin^2(x)} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, we go back to our substitution x= tan^1(1/5) take tan of both sides , and we get tan(x) = 1/5 now we can draw up a general right angle triangle and mark an angle x , and fill in the lengths 1 and 5 for thre opposite and adjacent sides respectively remember tan = opposite/adjacent

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0note the hypotenuse is sqrt(26)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now from that triangle we can find the value of sin(x) and cos(x) , the then you just plug them into the expression we had above

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so \[\sin(x) = \frac{1}{\sqrt{26}}\] \[\cos(x) = \frac{5}{\sqrt{26}}\] just by using the definitions

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so , our whole expression was\[\tan(2x \frac{\pi}{4}) = \frac{ \frac{ 2\sin(x)\cos(x) }{\cos^2(x)\sin^2(x) } 1}{ 1+ \frac{2\sin(x)\cos(x)}{\cos^2(x)\sin^2(x)}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then sub in the values for sin(x) and cos(x) above, and simplify

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0good. it worked out well. thanx man!
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