If cos − 1 x − cos − 1 2 y = α , then 4 x 2 − 4 x y cos α + y 2 is equal to

cos − 1 x − cos − 1 2 y = α cos − 1 ( 2 x y + ( − x 2 ) ( 1 − 4 y 2 ) ) = α cos − 1 ( 2 x y + 4 − y 2 − 4 x 2 + x 2 y 2 ) = α ⇒ 4 − y 2 − 4 x 2 + x 2 y 2 = 4 cos 2 α + x 2 y 2 − 4 x y cos α ⇒ 4 x 2 + y 2 − 4 x y cos α = 4 sin 2 α

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Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsGeneral ( General, Domain, Range & Graph)Medium2 minPYQ_2005

MathematicsMediumsingle choice

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

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Solution:

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

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:General ( General, Domain, Range & Graph)

⏱ 2mℹ️ Source: PYQ_2005

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