I had to solve for x in this

Aleah Choi

Aleah Choi

Answered question

2022-03-29

I had to solve for x in this equation:
sin(2x)tan(x)=sin(2x)

Answer & Explanation

aznluck4u72x4

aznluck4u72x4

Beginner2022-03-30Added 16 answers

As I'm sure you know you can not divide by zero. The function sin2x can equal zero so you should not divide by it. Instead you should factorize as follows:
sin2xtanx=sin2x
sin2xtanxsin2x=0
sin2x(tanx1)=0
Hence: sin2x=0  or  tanx=1
Then solve those two separately:
sin2x=02x=4π, 3π, 2ππ, 0, π, 2π, 3π, 4π
or
tanx=1x=7π4,3π4,π4,5π4
so:
x=2π,7π4,3π2,π,3π4,π2,0,π4,π2,π,5π4,3π2,2π

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