Question

Express sec(2x) and tan(2x) in terms of tan x . Hence, solve the equation " 2 tan (x) + sec (2x) = 2 tan (2x) "

Answer 1

I know how to express tan (2x) in terms of x, but sec 2x is escaping me. The furthest I have got is:

\[\frac{ 1 }{ 2\cos^2-1 } = 1 + \tan 2x^2\]

Thanks in advance!

Answer 2

Well, not perfectly true. Previously I reached the conclusion that:

\[\sec 2x = \frac{( \tan^2 +1) ^2}{ (1- \tan^2 ) ^2}\]

But plugging it into the latter part of the question became so convoluted that I am sure that this is not correct.

Answer 3

\[\large \bf \sec2x=\frac{1}{\cos2x}=\frac{1+\tan^2x}{1-\tan^2x}\]

Answer 4

\[\large \bf \tan2x=\tan(x+x)=\frac{tanx+tanx}{1-(tanx)(tanx)}=\frac{2tanx}{1-\tan^2x}\]

Answer 5

Hope you can solve your question !

Answer 6

Ah! I understand now! I see what you've done. Thank you for the insight! ;u;

Answer 7

No problem :D