Question

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

Solution

[

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}

]