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1. If ABCD is cyclic quadrilateral, show that AC . BD = AB . CD + BC . AD
2. In a ΔABC, show that a3 cos (B – C) + b3 cos (C – A) + c3 cos (A – B) = 3 abc
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4 Answers
622nd one is simple to start...
a = 2R sin A = 2R sin (B+C)
Expand:2 sin(B+C)cos(B-C) = sin 2B + Sin 2C
NOw sin 2B= 2 sin B cos B
Now apply 2R sin B = b
so you will now be able to use a cos B + b cos A = c
Then it should be easy...
Hope you can fill the gaps...
62THe first one is ptolmey's theorem.. which i remember having seen a couple of not so elegant proofs... [2]