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Find the solution of the equation: arcsin(sqrt2x)=arccos(sqrtx)

 Feb 6, 2015

Best Answer 

 #1
avatar+118723 
+5

arcsin(sqrt(2x))=arccos(sqrtx)      [I wasn't sure if the x is square rooted or not]

Okay I have to think these through the long way.

These are angles so the angle is the same so I called the angle theta and draw this pic

[I know theta has to be acute because it is the only posibility for acos and asin to have the same sign. ]

so 

$$\\1^2=2x+x\\
1=3x\\
x=1/3$$

 Feb 6, 2015
 #1
avatar+118723 
+5
Best Answer

arcsin(sqrt(2x))=arccos(sqrtx)      [I wasn't sure if the x is square rooted or not]

Okay I have to think these through the long way.

These are angles so the angle is the same so I called the angle theta and draw this pic

[I know theta has to be acute because it is the only posibility for acos and asin to have the same sign. ]

so 

$$\\1^2=2x+x\\
1=3x\\
x=1/3$$

Melody Feb 6, 2015

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