Hi Sahil,
The text version of the answer is -
Find the principal value of tan-1(tan〖2π/3〗 )
Let y = tan-1(tan〖2π/3〗 )
tan y =〖 tan〗〖2π/3〗
tan y = tan (120°)
We know that range of principal value of tan-1 is
(− π/2 , π/2 ) i.e. (− 90° ,90°)
Hence y = 120° not possible
Now,
tan y = tan (120°)
tan y = tan (180° – 60°)
tan y = – tan (60°)
tan y = tan (–60°)
tan y = tan (–60 × π/180)
tan y = tan ((-π)/3)
Hence, y = (-π)/3
Which is in the range of principal value of tan-1 i.e. ((-π)/2, π/2)
Hence, tan-1(tan〖2π/3〗 ) = y = (-π)/3
Notes -
(As tan (180 – θ) = – tan θ)
(As tan (–θ) = – tan θ)
Range |
|
sin-1 |
[-π/2, π/2] |
cos-1 |
[0,π] |
tan-1 |
(-π/2, π/2) |
Written on Jan. 26, 2017, 11:23 a.m.