Question

The minimum value of \(3^{sin^2 x} + 3^{cos^2 x}\), x ∈ R is

(a) \(\frac12\)

(b) 3 

(c) 6 

(d) 2√3

Answer 1

(d) 2√3

For all x∈R, \(3^{sin^2 x} >0, 3^{cos^2 x}>0\)

∴ AM > GM 

(∴ sin²x + cos²x = 1)