A Staircase Trigonometric Inequality

★ 8/10trigonometryTrigonometric IdentitiesEstimationinequality

Problem

Let 0<x<y<z<π20<x<y<z<\dfrac{\pi}2. Prove that

π2+2sin⁡xcos⁡y+2sin⁡ycos⁡z>sin⁡2x+sin⁡2y+sin⁡2z.\frac{\pi}2+2\sin x\cos y+2\sin y\cos z>\sin 2x+\sin 2y+\sin 2z.

Answer

Solution

Difficulty8/10
Topicstrigonometry, Trigonometric Identities, Estimation, inequality

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments
Log in to join the discussion.

No comments yet.