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If a,b,c,d are in geometric sequence th...

If a,b,c,d are in geometric sequence then prove that `(b-c)^(2) +(c-a)^(2) -(d-b)^(2)=(a-d)^2`

Text Solution

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`asin^2x+b(1-sin^2x)=c`
`:. (a-b)sin^2x=c-b`
Also, `a(1-cos^2x)+bcos^2x=c`
`:. (b-a)cos^2x=c-a`
`:. tan^2x=(c-a)/(b-d)`
Similarly, `tan^2y=(d-a)/(b-d)`
`:. a^2/b^2=tan^2y/tan^2x=(d-a)/(b-d)xx(c-a)/(b-c)`
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