SOLUTION: If sinx+cosx=1.2, then what is the value of {{{ sin^3 (x) + cos^3 (x) }}}?

Question 1113580: If sinx+cosx=1.2, then what is the value of ?
Answer by ikleyn(52887) (Show Source): You can put this solution on YOUR website!
.

You are given

sin(x) + cos(x) = 1.2.         (1)


Square both sides.  You will get


 = ,   or, replacing   by 1


1 + 2*sin(x)*cos(x) = 1.44,    which implies


sin(x)*cos(x) =  = 0.22.     (2)


Now we are ready to calculate  .


Use the formula   = .  It gives you 


 = ..


Now replace in this formula  sin(x) + cos(x) by 1.2 (since it is given); next replace    by 1  and  sin(x)*cos(x)  by 0.22, 

based on (2).  Then you get    = 1.2*(1-0.22) = 0.936.


Answer.   = 0.936.

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