SOLUTION: The equation (sin x)^6 +(cos x)^6=a has a real solution for which of the below mentioned cases:- A.0.5<=a<=1 B.0.25<=a<=0.5 C.-1<=a<=1 D.0<=a<=0.5

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Question 31496: The equation (sin x)^6 +(cos x)^6=a has a real solution for which of the below mentioned cases:-
A.0.5<=a<=1
B.0.25<=a<=0.5
C.-1<=a<=1
D.0<=a<=0.5

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
The equation (sin x)^6 +(cos x)^6=a
A={(SINX)^2+(COSX)^2}^3-3*((SINX)^2)*((COSX)^2)*((SINX)^2+(COSX)^2)
=1-3*((SINX)^2)*((COSX)^2)=1-(3/4)*{(SIN(2X))^2
=1-0=1...MAXIMUM......AND.........
=1-1*3/4=0.25...MINIMUM
ANSWER IS A AND B