in ABC show that sin^2A/2+sin^2B+C/2=1
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Step-by-step explanation:
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!!
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