Integrate #\int {sin(2x)}/{sinx}dx# ?

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Answer 1 · 2018-06-21T20:48:24

# int \ sin(2x)/sinx \ dx =2 sinx + C #

We seek:

# I =int \ sin(2x)/sinx \ dx #

Using the double angle formula:

# sin 2x -= 2sinxcosx #

We can write:

# I =int \ (2sinxcosx)/sinx \ dx #

# \ \ =2 \ int \ cosx \ dx #

# \ \ =2 sinx + C #

Answer 2 · 2018-06-21T20:50:21

#I=2sinx+c#

We know that,

#color(blue)((1)sin2theta= 2sinthetacostheta#

Here,

#I=int(sin2x)/sinx dx...tocolor(blue)( Apply(1)#

#=int(2sinxcosx)/sinx dx#

#=int2cosx dx#

#I=2sinx+c#