SOLUTION: If sinx+cosx=-1/5, and {{{ 3pi/4 }}}≤x≤pi, find the value of cos2x.

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Question 1113956: If sinx+cosx=-1/5, and ≤x≤pi, find the value of cos2x.
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
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If  sinx + cosx = -1/5,   then, squaring both sides


 = ,   or,  replacing   by 1

1 + 2*sin(x)*cos(x) = ,  and hense

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



Since  2*sin(x)*cos(x) = sin(2x),  you get

sin(2x) = .



Next, since   <= x <= , you have  for 2x    <= 2x <= ,  i.e.  2x lies in QIV.


Therefore,  cos(2x) =  =  =  =  =  = .


The sign at sqrt is "+" (plus)  since cosine is positive in QIV.


Answer.  cos(2x) = .


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