How to solve the Trigonometric Equation of? (2sin(x) - 1)(tan(x) - 1) = 0 for 0 ≤ x ≤ 2 pi

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Answer 1 · 2018-02-24T20:18:21

#color(blue)(x=pi/6,(5pi)/6,pi/4,(5pi)/4)#

#(2sinx-1)(tanx-1)=0#

Both brackets need to be equal to zero:

First bracket

#2sinx-1=0#

Add #1# to both sides:

#2sinx=1#

Divide both sides by #2#

#sinx=1/2#

#x=arcsin(sinx)=arcsin(1/2)=>x=pi/6,(5pi)/6#

Second bracket:

#(tanx-1)=0#

Add #1# to both sides:

#tanx=1#

#x=arctan(tanx)=arctan(1)=>x=pi/4,(5pi)/4#

So solutions are:

#color(blue)(x=pi/6,(5pi)/6,pi/4,(5pi)/4)#