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Prove that sin squareA / 2 + sin square B / 2 + sin square C/2 = 1- r / 2R |
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Answer» DEAR Student, Taking LHS: =Sin^2 A/2+sin^2 B/2+sin^2 C/2 =1-cos^2 A/2 +sin^2 B/2+sin^2 C/2 =1-(cos(A+B)/2 cos(A-B)/2) + sin^2 C/2 = 1-(cos(pi-C)/2 cos(A-B)/2)+sin^2C/2 = 1+sin C/2(sin C/2 -cos(A-B)/2) =1+sin C/2(sin(pi –(A+B)/2 -cos(A-B)/2) =1+sin C/2(cos (A+B)/2-cos(A-B)/2) =1+sin C/2(-2sinA/2 sinB/2) = 1-2sinA/2 sin B/2 sin C/2 =RHS [hence PROVED]. CHEERS!! Regards, VIKAS (B. Tech. 4th year Thapar University) |
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