a cosA +b cosB + c cosC=2asinB.sinC=8(delta)square/abc.

Asked by Bidyashree Rout | 13th Feb, 2014, 07:58: AM

Expert Answer:

 
We know that the area of the triangle
A r e a comma space triangle equals 1 half a b sin C rightwards double arrow sin C equals fraction numerator 2 triangle over denominator a b end fraction comma space w h e r e space triangle space i s space t h e space a r e a space o f space t h e space t r i a n g l e. rightwards double arrow fraction numerator 2 triangle over denominator a b end fraction equals sin C S i m i l a r l y comma space w e space h a v e comma space sin B equals fraction numerator 2 triangle over denominator a c end fraction s u b s t i t u t i n g space t h e space v a l u e space o f space sin C space a n d space sin B comma w e space h a v e a cos A plus b cos B plus c cos C equals 2 a cross times fraction numerator 2 triangle over denominator a b end fraction cross times fraction numerator 2 triangle over denominator a c end fraction equals fraction numerator 8 triangle squared over denominator a b c end fraction

Answered by  | 14th Feb, 2014, 11:02: PM

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