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shubhamsrg
 3 years ago
how to prove :
sin^3 x + cos ^3 x <= 1
shubhamsrg
 3 years ago
how to prove : sin^3 x + cos ^3 x <= 1

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Did you learn integration before?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Use integration to find the critical points and take that back to your equation sin^3(x)+cos^3(x). But I think it should be not less than 1

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0didnt get you..please elaborate ..

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0let f(x)=sin^3(x)+cos^3(x), then f'(x)=3sin^2(x)cos(x)3cos^2(x)sin(x) and solve f'(x)=0 for x and use x to find the maximum or minimum of f(x).

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0fair enough i guess.. i got x=0,pi/2 and pi/4 0 and pi/2 yield f(x) =1 and the other one gives 1/sqrt(2) seems correct !! hmm..

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0in the mean time,,i came across this : we know sin^2x ( sinx 1) <= cos^2x ( 1 cosx) equality will hold for x=0 or pi/2 so, sin^3 x  sin^2 x <= cos^2x  cos^3x => sin^3x + cos^3 c <= 1 !!!!!!!!!!!!!!!!!

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0thanks,,@NewbieCarrot
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