UP TGT Mathematics Trigonometry Test Series - Part 2
In ΔABC, a sin(B - C) + b sin(C - A) + c sin(A - B) is equal to:
Type: MCQ • Marks: 1
In ΔABC, a sin(B - C) + b sin(C - A) + c sin(A - B) is equal to:
Options
A. 0
B. 1
C. a + b + c
D. abc
Explanation
By Sine Rule, a = 2R sin A = 2R sin(B+C). So a sin(B-C) = 2R sin(B+C) sin(B-C) = 2R (sin²B - sin²C). Sum = 2R (sin²B - sin²C + sin²C - sin²A + sin²A - sin²B) = 0.
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