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

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MathematicsInverse Trigonometric FunctionsSum And Difference Of AnglesMedium2 minPYQ_2015

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

Stream:BITSATSubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Sum And Difference Of Angles

⏱ 2mℹ️ Source: PYQ_2015

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