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If a^2,b^2,c^2 are in A.P., prove that c...

If `a^2,b^2,c^2` are in A.P., prove that `cotA ,cotB ,cotC` are in `AdotPdot`

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Let `cotA,cotB and cotC` are in `A.P.`
Then, `2cotB = cotA+cotC`
`=>2cosB/sinB = cosA/sinA+cosC/sinC->(1)`
We know,
`sinA/a = sinB/b = sinC/c = k`
`=>sinA = ka, sinB = kb, sinC = kc`
So, (1) becomes,
`2[(a^2+c^2-b^2)/(2ac)]*1/(kb) = [(b^2+c^2-a^2)/(2bc)]*1/(ka) +[(a^2+b^2-c^2)/(2ab)]*1/(kc) `
...
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RD SHARMA ENGLISH-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-All Questions
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