Forum - Trigonometry

Trigonometric inequation

Marion
Visitor
2015-10-25 18:42:52
#1
Demonstrate that
sin8 x + cos8x ? 1/8

 

RE: Trigonometric inequation

Marion
Visitor
2015-10-25 18:44:08
#2
sin8x + cos8x ≥ 1/8

Trigonometric inequation - I hope this will help

Steve
Visitor
2015-10-25 18:48:27
#3
((sinx)2+(cosx)2)4=(sinx)8+(cosx)8+4(sinx)2.(cosx)2((sinx)4+(cosx)4)+6(sinx)4.(cosx)4=1.

The max value of the SUM sinx+cosx is for x=45° and sinx=cosx=1/&rad;2. In this case we have
(sinx)8+(cosx)8=1-(4.(1/4).(1/4+1/4)-6/4.1/4)=1-(1/2+3/8)=1/8
and this is the smallest value o the expression (sinx)8+(cosx)8
then
(sinx)8+(cosx)8 ≥ 1/8
 
 

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