Questions
If A,B,C are the angles of a triangle , the system of equations has
detailed solution
Correct option is B
Let Δ=sinA111sinB111sinC Applying C2→C2−C1 and C3→C3−C1 we get Δ=sinA1−sinA1−sinA1sinB−1010sinC−1 Expanding along C3, we get Δ=(1−sinA)1sinB−110+(sinC−1)sinA1−sinA1sinB−1=(1−sinA)(1−sinB)+(sinC−1)[sinA(sinB−1)−(1−sinA)]=sinA(1−sinB)(1−sinC)+(1−sinA)(1−sinB)+(1−sinA)(1−sinC)Since A,B,C are the angles of a triangle 0< sinA, sin B, sin C≤1. Also , at most one of sin A, sin B, sin C can be equal to 1. Thus , at most two of three terms in Δ can be zero and remaining must be positive . Therefore, Δ>0 Hence , the given system of equations has a unique solution.Similar Questions
The number of solutions of
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