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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......(i) `
We know, `sinA/a=sinB/b=sinC/c=k `
`⇒sinA=ka,sinB=kb,sinC=kc ......(ii)`
Thus by cosine formula
`2ab cos C=a^2+b^2-c^2...(iii)`
`2ac cos B=a^2+c^2-b^2...(iv)`
...
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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
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  14. In A B C , prove that (a – b)^2 cos^2 C/2 + (a + b)^2 sin^2 C/2 =c^2d...

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