what is the maximum value of

Question

sin^50 x+cos^60 x and how to do it?  

Answer 1

F=sin^50 x+cos^60 x

dF/dx=50 sin^49xcosx+60 cos^50 x(-sinx)

dF/dx=0

50 sin^49xcosx-60 cos^50 x(sinx)=0

50 sin^49xcosx=60 cos^50 x(sinx)

50 sin^48x=60 cos^49 x

sin^48x/ cos^49 x=60/50

tan^48xsecx=1.2

tan^48x=1.2 or secx=1.2

tanx=0.02

x=1.146⁰

At x=1.146⁰ F is maximum

F=sin^50 (1.146⁰ )+cos^60 (1.146⁰ )

   =1.115*10^-85+0.988

   =0.988