Solve $\cos 2x = \dfrac{1}{2}$ for $0^\circ \le x \le 180^\circ$.
A$x = 30^\circ$ only
B$x = 30^\circ$ or $150^\circ$CORRECT
C$x = 60^\circ$ or $300^\circ$
D$x = 60^\circ$ or $120^\circ$
JUPEBMathematicsTrigonometry
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Why the answer is B, and why the others tempt you.
Since $0^\circ \le x \le 180^\circ$, $2x$ lies between $0^\circ$ and $360^\circ$. $\cos 2x = \dfrac{1}{2}$ gives $2x = 60^\circ$ or $300^\circ$, so $x = 30^\circ$ or $150^\circ$. Forgetting to halve gives the values of $2x$, and stopping after the principal value misses $150^\circ$.
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