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Question

If A,B and C represents the angles of a triangle, then cosA+cosB+cosC1 equal to


Your Answer
A
4sinA2sinB2sinC2
Correct Answer
B
4sinA2sinB2sinC2
Your Answer
C
4cosA2cosB2cosC2
Your Answer
D
4cosA2cosB2cosC2

Solution

The correct option is A 4sinA2sinB2sinC2
(cosA+cosB)+cosC1=2cosA+B2cosAB2+cosC1=2cosπC2cosAB2+cosC1=2sinC2cosAB2+12sin2C21=2sinC2[cosAB2sinC2]=2sinC2[cosAB2sinπ(A+B)2]=2sinC2[cosAB2cosA+B2]=2sinC2[2sinA2sinB2]=4sinA2sinB2sinC2 
 

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