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Question
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
Options
a2 b2
ab
a4 b4
a2 + b2
Solution
Given:
`x= a cosθ, y= b sin θ`
So,
`b^2 x^2+a^2 y^2`
= `b^2(a cos)^2+a^2(b sin θ)^2`
=` b^2 a^2 cos^2θ+a^2 b^2 sin^2θ`
=`b^2a^2 (cos^2 θ+sin^2θ)`
We know that,
`sin^2θ+cos^2θ=1`
Therefore,` b^2x^2+a^2y^2=a^2b^2`
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