this is a question that was part of an mcq test. and i did'nt have any clue as to how to begin! finally i just tried plugging in values for A,B,C to see if they worked. for ex. i put A=B=C=60 (degrees)- equilateral and so on..but i'd like to know the logical way to do it... if A,B,C are the vertices of a triangle, and if cosBcosC + sinAsinBsinC = 1 is the triangle a) equilateral b) isosceles c) right angled isosceles d) right angled but not isosceles e) none of the above.
Right, I'm assuming you know sin^2 +cos^2 = 1. Well you can see this is nearly similar, and almost exactly the same if B = C. So there's two angles the same. So now cos^2 + sinA sin^2 = 1 Which means sinA must be 1. Therefore A can only take value of 90 degrees - right angle (450...etc useless here) 180 - 90..other two angles combine as total 90 degrees, so they must be 45 each since you've already found they're the same. Which leaves you a right angled isosceles.