CBSE Class 10 Answered
cos2A+cos2B-cos2C=1-4sinAsinBsinC
Asked by irenegladis | 05 Apr, 2009, 09:08: AM
Expert Answer
we know that cos u - cos v =-2 sin(u+v)/2 sin(u- v)/2
cos2A-cos2C = -2sin(A+C) sin(A-C) = -2 sinB sin(A-C)
and cos2B = 1 - 2sin2B
cos2A+cos2B-cos2C= -2 sinB sin(A-C) +1 - 2sin2B
=1 - 2sinB (sin(A-C) + sinB )
=1- 2 sinB 2sin(A-C+B) /2 cos(A-C-B)/2
=1 - 4 sinB sin(π-C-C) /2 cos(A-(π-A))/2
=1- 4 sinB cosC sinA
so instead of sinC, cosC will be there.
Answered by | 09 Apr, 2009, 02:33: AM
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