If sides a, b, c of △ABC (with a opposite A, etc) are in arithmetic progression, then prove that
3tanA2tanC2=1
My attempt:
a, b, c are in arithmetic progression, so
2b=a+c2sinB=sinA+sinC2sin(A+C)=2sinA+C2cosA−C22sinA+C2cosA+C2=sinA+C2cosA−C22cosA+C2=cosA−C2
Answer
Expand your last line: 2(cosA2cosC2−sinA2sinC2)=(cosA2cosC2+sinA2sinC2)
and your result is immediate after a cancellation.
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