A Cosecant Product

★ 8/10trigonometryTrigonometric Identities

Problem

Suppose

∏k=145csc⁡2(2k−1)∘=mn,\prod_{k=1}^{45}\csc^2(2k-1)^\circ=m^n,

where m,n∈N∗m,n\in\mathbb N^{*} with m,n⩾2m,n\geqslant 2. Find m+nm+n. (Hint: use sin⁡3x=4sin⁡xsin⁡(60∘−x)sin⁡(60∘+x)\sin 3x=4\sin x\sin(60^\circ-x)\sin(60^\circ+x).)

Answer

Solution

Difficulty8/10
Topicstrigonometry, Trigonometric Identities

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.