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If cos2B=(cos(A+C))/("cos"(A-C)), then t...

If `cos2B=(cos(A+C))/("cos"(A-C))`, then `tanA ,t a n B ,tanC` are in

(a)A.P.

(b) G.P.

(c) H.P.

(d) none of these

Text Solution

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`(cos2B)/1=(cos(A+C))/(cos(A-C))`
`(cos2B+1)/(cos2B-1)=(cos(A+C)+cos(A-C))/(cos(A+C)-cos(A-C))`
`(2sin^2B)/(2cos^2B)=(2sinAsinC)/(2cosAcosC)`
`tan^2B=tanAtanC`
`tanA/tanB=tanB/tanC`.
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