Question

inverse trig identity...

Answer 1

prove.
\[2\tan^{-1}(\frac{ 1 }{3 }) + \tan^{-1} (\frac{ 1 }{ 7 }) = \sec^{-1}(\frac{ \sqrt{34} }{ 5} ) + \sec^{-1}(\frac{ \sqrt{17} }{4 })\]

Answer 2

I can prove it by solving both sides... but I want to know how to prove it by simplifying only a one side or using a short method .... pls help!

Answer 3

ganeshi8 any idea ?

Answer 4

@hartnn , @ganeshie8

Answer 5

Can u guys at least give me a hint... ? :-(

Answer 6

both sides on that identity simplify in to \[\frac{ \pi }{ 4 }\]
so... u can prove it if u simplify both sides... but it's not the way i'm looking for.. :-(

Answer 7

Try to use the identity for tan(a+b)

Answer 8

arctan to arcsec , hmmm

arctan to arcsin : arctan x = arcsin(x/ sqrt (x^2+1))

arcsin to arccsc x : arccsc (1/x) = arcsin x

arccsc to arcsec : arcsec x = pi/2 - arccsc x