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If cos^4 x / cos^2 y + sin^4 x / sin^2 y = 1 then prove that cos^4 y / cos^2 x + sin^4 y / sin^2 x=1.
If cos^4 x / cos^2 y + sin^4 x / sin^2 y = 1 then prove that cos^4 y / cos^2 x + sin^4 y / sin^2 x=1.

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2 years ago

```							the question is a tricky one for sure, but once you see how it is solved, there is nothing to it.first start by multiplying cos^4 x / cos^2 y + sin^4 x / sin^2 y = 1 by sin^2y*cos^2ythen write sin^2y as 1-cos^2y.it becomes cos^2(1-cos^2y)=cos^4x+cos^2y(sin^4x-cos^4x)=cos^4x+cos^2y(sin^2x-cos^2x)or cos^4y+cos^4x-2cos^2xcos^2y=0or (cos^2x-cos^2y)^2=0or cos^2x=cos^2yand sin^2x=sin^2yNow, cos^4 y / cos^2 x + sin^4 y / sin^2 x=cos^2y+sin^2y=1 Hence proved
```
2 years ago
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