Question #ab74b

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Answer 1 · 2017-07-31T17:45:53

$theta = pi/2, (2pi)/3, (4pi)/3$

$2sin theta cos theta+sin theta - 2cos theta-1=0$

$2sin theta cos theta - 2cos theta +sin theta -1=0$ $->$ rearrange the terms

$2 cos theta (sin theta - 1) +1(sin theta -1)=0$ $->$ factor

$(sin theta - 1)(2 cos theta +1) = 0$ $->$ factor out $sin theta - 1$

There are two possibilities:

$sin theta - 1 = 0$

$sin theta = 1$
$theta = pi/2$

$2 cos theta + 1 = 0$

$2 cos theta = -1$
$cos theta = -1/2$
$theta = (2pi)/3, (4pi)/3$

So, $theta = pi/2, (2pi)/3, (4pi)/3$ .