csat-suneung 2017 Q25

csat-suneung · South-Korea · csat__math-science 3 marks Standard trigonometric equations Solve trigonometric equation for solutions in an interval
When $0 < x < 2 \pi$, the sum of all real roots of the equation $\cos ^ { 2 } x - \sin x = 1$ is $\frac { q } { p } \pi$. Find the value of $p + q$. (Here, $p , q$ are coprime natural numbers.) [3 points]
When $0 < x < 2 \pi$, the sum of all real roots of the equation $\cos ^ { 2 } x - \sin x = 1$ is $\frac { q } { p } \pi$. Find the value of $p + q$. (Here, $p , q$ are coprime natural numbers.) [3 points]