Question

Find minimum value of f(x)=cos²x + sec²x.

Answer 1

We know that cos2x,sec2x≥0

hence by using AM≥GM for positive numbers cos2x & sec2x

cos2x+sec2x2≥(cos2x⋅sec2x)1/2

cos2x+sec2x2≥(1)1/2

cos2x+sec2x2≥1

cos2x+sec2x≥2

∴Min(cos2x+sec2x)=2