Question

can someone solve:
tan^-1(tan(pi/4-x/2))=?
-pi/2<=x<=3pi/2

Answer 1

shld it be pi/4-x/2

Answer 2

\[\large \tan^{-1}(\tan(x)) = x\] This rule applies to cosines and sine functions as well. The inverse function always outdoes the function itself.

Answer 3

so what do you say my answer is right or not

Answer 4

You are absolutely right.

Answer 5

then u know range of inverse tan
(-pi/2,pi/2)

Answer 6

now x/2 has range [-pi/4,3pi/4] as per my question

Answer 7

range of inverse tangent = \(\large (\frac{\pi}{2} , \frac{-\pi}{2})\)

Answer 8

ohk i got myself cleared
i was confused between tan^-1(x) and tan^-1(tanx) as for both range will varry
thanks a lot Jhannybean

Answer 9

Good job, :)