Solving 37tan3x = 11tanx

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I sometimes feel the authors scam us when they say, solution is left for the readers.

kushaldey

I think you overcomplicate the 2nd method. The way you do it leads to a cubic in sinx. You can apply the product-to-sum when you cross-multiply: 37sin3xcosx = 11sinxcos3x and since 2sin𝛼cos𝛽=sin(𝛼+𝛽)+sin(𝛼-𝛽) you get which if you go with 2x=y is a simple quadratic in siny without even a constant term.

randomjin

Isn't inverse tangent an odd function? Seems like you could combine the two non-zero solutions.

francis

for anyone looking for the solution via the 2nd method..
you will get sinx(25 - 26sin^2(x)) = 0
this gives
x = npi
and
x = sin^-1 (+-5 / sqrt(26))

Jha-s-kitchen

All the best man, ,
Regards from India, ,
Following your channel from few days and content was good

rahul.g

I transformed the tangents to sines and cosines and got arccos(2/sqrt5) and arccos(-2/sqrt5) but i don't know that's correct :b.

eduardosebastianlunarodrig

Огромное спасибо.Красивое решение.Привет из Баку.

elmurazbsirov

If you left out the multiple inane statements and commentary, you could have fit both solutions into the video and still kept it under 10 minutes.

XJWill

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