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4-1.Complex numbers
medium
$\frac{{(\cos x + i\sin x)(\cos y + i\sin y)}}{{(\cot u + i)(1 + i\tan v)}}$ ને $A + iB$ સ્વરૂપમાં લાવો.
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
એકપણ નહીં.
Solution
(a)$L.H.S.$ $ = \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)]$
Standard 11
Mathematics
