How do you find the general solutions for #tanx = 2sinx#?

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Answer 1 · 2015-08-13T02:09:24

#tanx = 2sinx#

#tanx - 2sinx =0#

#sinx/cosx - 2sinx =0#

#sinx(1/cosx -2) =0#

#sinx =0" "# or #" "1/cosx-2=0#

#sinx =0" "# or #" "cosx=1/2#

#sinx = 0# #hArr# #x=pin# for #n# an Integer.

#cosx=1/2# #hArr# #x = pi/3 +2pin# #" or "# #x = -pi/3 +2pin#

The solutions are:

#{: (x = pi n), (x = pi/3 +2pi n), (x = - pi/3 +2pi n):} }# for #n# an Integer.