If cos−1x−cos−12y =α, then 4x2−4xycosα +y2 is equal to

Given, cos−1x−cos−12y =α⇒cos−1(2xy+(1−x2)(1−4y2 ) )=α ⇒cos−1(2xy+4−y2−4x2+x2y2 )=α ⇒2cosα=xy+4−y2−4x2+x2y2⇒4x2+y2−4xycosα =4sin2α

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If ^{ -1 }{ x } - ^{ -1 }{ { y }{ 2 } } = , then 4{ x }^{ 2

Question

If $cos^{- 1} x - cos^{- 1} \frac{y}{2} = α$ , then $4 x^{2} - 4 x y cos α + y^{2}$ is equal to

2 sin 2 α

4

4 sin^{2} α

- 4 sin^{2} α

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Sebastian Discussed

cos^{- 1} x - cos^{- 1} \frac{y}{2} = α

, then

4 x^{2} - 4 x y cos α + y^{2}

is equal to

13 mins ago

Discuss this question LIVE

13 mins ago

Given,

cos^{- 1} x - cos^{- 1} \frac{y}{2} = α

\Rightarrow cos^{- 1} (\frac{x y}{2} + (1 - x^{2}) (1 - \frac{y ^{2}}{4})) = α

\Rightarrow cos^{- 1} (\frac{x y + 4 - y ^{2} - 4 x ^{2} + x ^{2} y ^{2}}{2}) = α

\Rightarrow 2 cos α = x y + 4 - y^{2} - 4 x^{2} + x^{2} y^{2}

\Rightarrow 4 x^{2} + y^{2} - 4 x y cos α = 4 sin^{2} α

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Question Text	If $cos^{- 1} x - cos^{- 1} \frac{y}{2} = α$ , then $4 x^{2} - 4 x y cos α + y^{2}$ is equal to
Answer Type	Text solution:1
Upvotes	150