If `x costheta=y sin theta=sqrt(x^(2)+y^(2))` and `(cos^(2)theta)/(a^(2))+(sin^(2)theta)/(b^(2))=(1)/(x^(2)+y^(2))`
then the value correct releation is (यदि `x costheta=y sin theta=sqrt(x^(2)+y^(2))` और `(cos^(2)theta)/(a^(2))+(sin^(2)theta)/(b^(2))=(1)/(x^(2)+y^(2))` है तो सही सम्बंद क्या होगा )

Options

A. `(x^(2))/(b^(2))-(y^(2))/(a^(2))=1`
B. `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
C. `(x^(2))/(b^(2))-(y^(2))/(a^(2))=1`
D. `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`

Answer

b

Explanation

`cos^(2)theta-sin^(2)theta=(1)/(3)` (given)
`cos^(2)theta+sin^(2)theta=1` (property)
`(cos^(2)theta-sin^(2)theta)(cos^(2)theta+sin^(2)theta)`
`=(1)/(3)xx1`
`cos ^(4)theta-sin^(4)theta=(1)/(3)`
`therefore ((a^(2)-b^(2))(a^(2)+b^(2))=a^(4)-b^(4))`