Question

# Consider the expression 3^{sin^6x}+3^{cos^6x} Find the minimum value.

Solution

@3^{sin^6x}+3^{cos^6x}are positive numbers And A.Mgeq G.M. frac{3^{sin^6x}+3^{cos^6x}}{2}geq sqrt{3^{sin^6+(cos^6x)}} 3^{sin^6x}+3^{cos^6x}geq 2sqrt{3^{1-frac{3}{4}sin^22x }} 3^{sin^6x}+3^{cos^6x}geq 2(sqrt{3frac{1}{4} } )=2.3^frac{1}{8} The correct answer is:2.3^frac{1}{8}