SOLUTION: If {{{cos(theta) = sqrt( 1/2 + 1/(2 * sqrt( 2 ))) }}} and {{{sin(theta) = sqrt( 1/2 - 1/(2 * sqrt( 2 ))) }}} with {{{0 <= theta < 2pi}}} it follows that {{{2theta}}} = .... {{{pi}

Question 1064475: If and with it follows that = ....
the answer is but I got only What did I do wrong?
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.
If and with it follows that = ....
the answer is but I got only What did I do wrong?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You correctly determined that  = .

Notice that both  and  are positive, as it is (implicitly) stated by the condition.


Hence,  lies in QI.


Therefore  can be one of the two angles:  or  and CAN NOT be anything different.


Moreover, since   < , the angle  is less than .


Therefore,  =  and CAN NOT be anything different.

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