3^sin^2(x)+3^cox^2(x)=2√3

Question

3^sin^2(x)+3^cox^2(x)=2√3

Answer 1

3^sin²x+3^(1-sin²x)-2√3=0
3^sin²x=a
a²-2√3a+3=0
(a-√3)²=0
a=√3
3^sin²x=√3
sin²x=1/2
(1-cos2x)/2=1/2
1-cos2x=1
cos2x=0
2x=π/2+πn,n∈z
x=π/4+πn,n∈z