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If asin^2x+bcos^2x=c,bsin^2y+acos^2y=d,a...

If `asin^2x+bcos^2x=c,bsin^2y+acos^2y=d,and atanx=btany`, then prove that `a^2/b^2=((d-a)(c-a))/((b-c)(b-d))`.

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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