perplexus.info :: Just Math : trigonometry and a triangle

trigonometry and a triangle (Posted on 2004-02-26)

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)

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Puzzle Thoughts

Comment 15 of 15 |

1=cos(a)cos(b)+sin(a)sin(b)sin(c)<=

<= sin(a)sin(b)+cos(a)cos(b)=cos(a-b) so a=b.

a,b>0, so equalityh holds iff sin(c)=1.

Hence A=B=45 deg. and, C =90 deg.

Posted by K Sengupta on 2023-06-19 02:06:14

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