Which of the following are solutions to the equation tan22x

Which of the following are solutions to the equation tan^2(2x) - 1=0? Check all that apply. -pi/8 3pi/8 pi/4 pi/2

Solution

tan²(2x)-1=0

add 1 on both sides

=>tan²(2x)-1+1=0+1

=>tan²(2x)=1

=>tan(2x)=-1,tan(2x)=1

=>2x=-pi/4,3pi/4,7pi/4 , 2x=pi/4,5pi/4

=>x=-pi/8,3pi/8,7pi/8 , x=pi/8,5pi/8

from the options -pi/8 ,3pi/8 are correct