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If y=A sin^2x+Bcos^2x then prove that si...

If `y=A sin^2x+Bcos^2x` then prove that `sin2x.y_(2)-2cos2x.y_(1)=0`
where `y=(dy)/(dx),y_(2)=(d^2y)/(dx^(2))`.

Text Solution

Verified by Experts

`y=Asin^2x+B cos^2`
`rArr y_(1)=A . 2 sinx cosx+B. 2 cosx(-sinx)`
`=A sin2x-Bsin2x=(A-B)sin2x`
`rArr y^2=(A-B)2cos2x`
Now, L.H.S. `=sin2x.y_(2)-2cos2x. Y_1`
`=sin2x .(A-B). 2cos 2x`
`-2cos2x. (A-B)sin2xx`
`=0= R.H.S.`
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