1.

If `x=asinthetaa n dy=btantheta,`then prove that `(a^2)/(x^2)-(b^2)/(y^2)=1`

Answer» We have
` x= a sin theta rArr (a)/(x)=(1)/(sin theta) rArr (a)/(x) = "cosec" theta " "...(i) `
` and y= b tan theta rArr (b)/(y)= (1)/(tan theta) rArr (b)/(y) = cot theta. " "...(ii) `
Squaring (i) and (ii) and subtracting, we get
`((a^(2))/(x^(2))- (b^(2))/(y^(2)))= ( "cosec"^(2)theta - cot^(2)theta ) =1. `
Hence, ` ((a^(2))/(x^(2))- (b^(2))/(y^(2)))=1. `


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