Solve (sinx)(tanx) = 3sinx for 0 < x < 2pi. Round your answers to the nearest hundredth of a radian ?

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Answer 1 · 2018-05-10T04:44:31

#x=3.14,x=1.25 or x=4.39#

Here,

#sinxtanx=3sinx,where, 0 < x < 2pi#

#=>sinxtanx-3sinx=0#

#=>sinx(tanx-3)=0#

#=>sinx=0 or tanx-3=0#

#sinx=0 or tanx=3#

#(1)sinx=0,where, 0 < x < 2pi#

So, #color(red)(x=pi=3.14^R#

#(2)tanx=3 > 0=>I^(st)Quadrant or III^(rd)Quadrant#

#(i)I^(st)Quadrant=>0 < x <= pi/2#

#=>color(blue)(x=tan^-1(3)=1.25^R=(71.57)^circ#

#(ii)III^(rd)Quadrant=>pi <= x <= (3pi)/2#

#=>color(blue)(x=pi+tan^-1 (3)=4.39^R=(251.57)^circ#