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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))`.

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To prove that \( \frac{a^2}{b^2} = \frac{(d-a)(c-a)}{(b-c)(b-d)} \), we start with the given equations: 1. \( a \sin^2 x + b \cos^2 x = c \) 2. \( b \sin^2 y + a \cos^2 y = d \) 3. \( a \tan x = b \tan y \) ### Step 1: Express \(\sin^2 x\) in terms of \(c\) and \(b\) ...
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