Question

Value of \[\tan (\frac{ 1 }{ 2 } \cos ^{-1}\frac{ \sqrt{5} }{3 })\]

Answer 1

@Yahoo! first find the value of
\[\tan ( \cos ^{-1}\frac{ \sqrt{5} }{3 })\]
could you find it?

Answer 2

\[\tan ( \tan ^{-1} \frac{ 2 }{ \sqrt{5} })\]

Answer 3

@Yahoo! I can see that you have closed your previous question before it was done. Please don't do this.
It's against the code of conduct
http://openstudy.com/code-of-conduct
Thanks

Answer 4

lol...@ash2326 i got...that answer....and was waiting...for...Sauravs method..

Answer 5

@sauravshakya Any Idea

Answer 6

@ash2326 ...()

Answer 7

CANT WE USE CALCULATOR?

Answer 8

No Calculator.)

Answer 9

let
\[x=\cos^{-1} (\frac{\sqrt 5}{3})\]
so we got
\[\tan x=\frac{2}{\sqrt 5}\]
now find
\[\tan (\frac x 2)\]
we know
\[\large \tan x=\frac{2\tan \frac x 2}{1-\tan^2 \frac x2}\]
now find tan x/2 from this

Answer 10

i think....this may be little easier:

\[\cos ^{-1} \frac{ \sqrt{5} }{ 3 } = 2x\]

Answer 11

it doesn't matter, you have to solve a quadratic at last. Substitute tan x/2 or tan x= y

Answer 12

i got this...)....

Answer 13

Which one shuld i choose

Answer 14

Both of them r in my option

Answer 15

the one which is positive

Answer 16

Why...

Answer 17

\[\frac{ \pm3 - \sqrt{5} }{ 2 }\]

Answer 18

since
\[x=\cos^{-1}\frac{\sqrt{5}}{3} \]
\[\text{x will lie in the range 0 to}\frac{\pi}{2} \text{since }\frac{\sqrt{5}}{3} \text{is positive }\]
so
\[\text{x/2 will also lie in the range 0 to}\frac{\pi}{2}\]
\[\large \text{tangent is positive in this range :)}\]

Answer 19

Got.....it............thxxxxx

Answer 20

welcome :)