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Question Number 119506 by bemath last updated on 25/Oct/20

\cos \frac{π}{5} \cos x + \sin \frac{π}{5} \sin x ⩽ \frac{\sqrt{2}}{2}

Answered by 1549442205PVT last updated on 25/Oct/20

\cos \frac{π}{5} \cos x + \sin \frac{π}{5} \sin x ⩽ \frac{\sqrt{2}}{2}

\Leftrightarrow \cos (x - \frac{π}{5}) ⩽ \cos \frac{π}{4}

\Leftrightarrow x - \frac{π}{5} ⩾ \frac{π}{4} + 2 m π

\Leftrightarrow \frac{π}{4} + 2 m π ⩽ x ⩽ \frac{7 π}{4} + 2 m π