The minimum value of ( 2 sin ^{2} theta+3 cos ^{2} theta ) is

[
begin{array}{l}
quad 2 sin ^{2} theta+3 cos ^{2} theta
=2left(sin ^{2} theta+cos ^{2} thetaright)+cos ^{2} theta
=2+cos ^{2} theta
end{array}
]
Menimum value ( 4 cos ^{2} theta ) is 0
( therefore ) hirnimum value of ( 2+cos ^{2} theta )
[
begin{array}{l}
=2+0
=2
end{array}
]