18.
2-4sin^2(x)=0
2=4sin^2(x)
sin^2(x)=2/4
sin^2(x)=1/2
sin(x)=sqrt(1/2) or sin(x)=-sqrt(1/2)
if sin(x)=sqrt(1/2) =>x=π/4+2π*k, x= 3π/4+2π*k
if sin(x)=-sqrt(1/2)=>x=5π/4+2π*k, x=7π/4+2π*k
all solutions:
x= π/+2π*k
x=3π/4+2π*k
x=5π/4+2π*k
x=7π/4+2π*k
22.
sec ^2 (x)-1=0
(sec (x)-1)(sec (x)+1)=0
if sec (x)-1=0 =>sec (x)=1=>x=2pi*k
if sec (x)+1=0 =>sec (x)=-1=>x=pi +2pi*k
solutions:
x=2π*k
x=π+2π*k
why is the solution 2π•k, where k is any integer: because sec has period of 2π
reminder:
Period of y=sin x is 2π
Period of y=cos x is 2π
Period of y=tan x is π
Period of y=cot x is π
Period of y=sec x is 2π
Period of y=csc x is 2π
