Question

least value of 4cosec^2x+9sin^2x​

Answer 1

Another way using AM-GM inequality: for positive a,b

a+b2≥ab−−√

Notice

4csc2x+9sin2x=(2cscx)2+(3sinx)2≥2⋅2cscx⋅3sinx=121sinxsinx=12

Therefore, we conclude that the minimum value is 12