Answer:
Step-by-step explanation:
tan x/2=-√3/3
sec²x/2-tan²x/2=1
sec²x/2-3/9=1
sec² x/2=1+1/3=4/3
cos² x/2=3/4
2cos² x/2=3/2
1+cos x=3/2
cos x=3/2-1=1/2=cos π/3,cos (2π-π/3)
x=π/3,5π/3
or
cos x=(1-tan²x/2)/(1+tan²x/2)=(1-1/3)(1+1/3)=(2/3)/(4/3)=1/2=cos π/3,cos (2π-π/3)
or x=π/3,5π/3
x=π/3
x/2=π/6
tan x/2=tan π/6=√3/3
so x=π/3 is an extraneous value.
x=5π/3 is the solution.
or
tan x/2=-√3/3=-1/√3=(-1/2)/(√3/2) [by dividing numerator and denominator by 2]
=-tan π/6=tan (π-π/6),tan (2π-π/6)
x/2=5π/6,11π/6
x=5π/3,11π/3,
now 11π/3 >2π
so x=5π/3
