Question

Solve:
2tan^-1(cosx)=tan^-1(2cosecx)

Answer 1

\[\LARGE 2\tan^{-1}(cosx)=\tan^{-1}(2cosecx)\]

Answer 2

can we take tan of both the sides?
\[\LARGE \cancel 2(cosx)=\cancel 2(cosecx)\]

Answer 3

not at all!

Answer 4

why?

Answer 5

if you take tan,
left = tan (2 arctan(cos x))
which is not 2 cos x

Answer 6

tan(arctanx)=x right?
and why isn't it 2 cosx ?what is it then?

Answer 7

there is obvious difference between tan (arctan) and tan (2 arctan)

Answer 8

I was just treating it as a constant,if it was tan2x then things might have been different

Answer 9

hmm...constant can't be taken out of inverse trigonometric functions.

Answer 10

I see,then how do proceed?

Answer 11

to*

Answer 12

i can think of this formula :
\(\large \arctan x = 2 \arctan \frac{x}{1+\sqrt{1+x^2}}\)

Answer 13

haven't heard of it :/

Answer 14

now you do, apply it on left side

Answer 15

\[\large 2\tan^{-1}x=\tan^{-1} \frac{2x}{1-x^2}\]
how about this?

Answer 16

\[\large \frac{2cosx}{1-\cos^{2}x}=\frac{2}{sinx}\]
gives x=pi/4

Answer 17

i have not heard of that formula but ift hats true, yes x= pi/4

Answer 18

\[\large \tan2x=\frac{2tanx}{1-\tan^2x}\]
you haven't heard of this?!

Answer 19

that i know, but what you have written in inverse form , i don't recall