How do you solve $sin^2 x= cos^2 x + 1/2$ ?

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Answer 1 · 2015-07-20T04:23:36

Solve $sin^2 x = cos^2 x + 1/2$

$cos^2 x - sin^2 x = - 1/2$
$cos 2x = - 1/2$ --> $2x = +- (2pi)/3 + k2pi$

$x = +- pi/3 + kpi$

Within interval $(0, 2pi)$ , there are 4 answers:
$pi/3; (pi/3 + pi) = 4pi/3 ; (- pi/3 + pi) = 2pi/3 ; 5pi/3$

How do you solve sin^2 x= cos^2 x + 1/2sin^2 x= cos^2 x + 1/2?