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If a=x ^2+ y^2 then (x-a)(y-a)+(x-y)^2 ^2 ^2 =1.

Question

If $a = x cos^{2} α + y sin^{2} α$ then $(x - a) (y - a) + (x - y)^{2} sin^{2} α cos^{2} α = 1$ .

True

False

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Elijah Discussed

a = x cos^{2} α + y sin^{2} α

then

(x - a) (y - a) + (x - y)^{2} sin^{2} α cos^{2} α = 1

11 mins ago

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11 mins ago

Text solutionVerified

Given

a = x cos^{2} α + y sin^{2} α

⟹ x - a = x - x cos^{2} α - y sin^{2} α = x (1 - cos^{2} α) - y sin^{2} α = x sin^{2} α - y sin^{2} α = (x - y) sin^{2} α

⟹ y - a = y - x cos^{2} α - y sin^{2} α = y (1 - sin^{2} α) - x cos^{2} α = y cos^{2} α - x cos^{2} α = - (x - y) cos^{2} α

(x - a) (y - a) + (x - y)^{2} + sin^{2} α cos^{2} α = - (x - y)^{2} sin^{2} α cos^{2} α + (x - y)^{2} sin^{2} α cos^{2} α = 0

So the given relation is

False

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Question Text	If $a = x cos^{2} α + y sin^{2} α$ then $(x - a) (y - a) + (x - y)^{2} sin^{2} α cos^{2} α = 1$ .
Answer Type	Text solution:1
Upvotes	150