wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The imaginary part of tan-1cosθ+isinθ


A

tanh-1sinθ

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

tanh-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

12tanh-1sinθ

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

12tanh-1sinθ


Find the imaginary part of the given expression:

Let tan-1cosθ+isinθ=x+iy ...(i)

tan-1cosθ-isinθ=x-iy ...(ii)

Subtracting (ii) from (i)

2iy=tan-1(cosθ+isinθ)-tan-1cosθ-isinθ

=tan-1cosθ+isinθ-cosθ+isinθ1+cosθ+isinθcosθ-isinθ

=tan-12isinθ1+cos2θ+sin2θ

=tan-1isinθ

=tanh-1sinθ

Imaginary part is 12tanh-1sinθ

Hence, option (C) is the correct answer.


flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Parametric Differentiation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon