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trigonometry and a triangle (Posted on 2004-02-26) Difficulty: 4 of 5
Prove that in a triangle ABC,:

sin(A)sin(B)sin(C) + cos(A)cos(B) = 1

implies:

A = B = 45 and C = 90.

See The Solution Submitted by mohan    
Rating: 2.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): solution | Comment 7 of 14 |
(In reply to re: solution by Federico Kereki)

Since the angles of a triangle add up to 180 degrees, no one angle can be greater than 180 degrees, sin(a)sin(b)>=0.  In fact equality is achieved only in the degenerate triangle where a and b are each zero degrees and c is 180, which is another "solution" if degenerate triangles are allowed.
  Posted by Charlie on 2004-02-27 07:22:17

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