Asked by avril

How do u solve equations like

sin 2x= tan 9x+3
Answered by drwls
Do you mean (tan9x) +3 or tan (9x+3) ?
Answered by Reiny
Wow, that is a nasty one.
Did you make it up or is that actually a question from a textbook?

I started breaking tan(9x) down into
tan(x+8x) and then started using the half-angle formulas to get tan 4x , then tan 2x, but the back-substitution became horrendous.

I sometimes use this very powerful
equation solver

http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=basic

It gave me about 18 real solutions for x, of course they would be all in radians
I used the interpretation

sin(2x) = tan(9x) + 3

I tested the first answer of x= 1.60579 and another x = 1.26517 and they both worked.

try it.
Answered by drwls
The answer depends upon your answer to my first question. It is a messy problem either way
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