Complex Numbers And Quadratic Equations question 438
Question: $ A+iB $ form of $ \frac{(\cos x+i\sin x)(\cos y+i\sin y)}{(\cot u+i)(1+i\tan v)} $ is [Roorkee 1980]
Options:
A) $ \sin u\cos v[\cos (x+y-u-v)+i\sin (x+y-u-v)] $
B) $ \sin u\cos v[\cos (x+y+u+v)+i\sin (x+y+u+v)] $
C) $ \sin u\cos v[\cos (x+y+u+v)-i\sin (x+y+u+v)] $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
L.H.S. $ =\frac{(\cos x+i\sin x)(\cos y+i\sin y)}{(\cos u+i\sin u)(\cos v+i\sin v)} $ $ \sin u\cos v $ $ =\sin u\cos v[\cos (x+y-u-v)+i\sin (x+y-u-v)] $
BETA
