If y = cos ( 3 π + cos − 1 2 x ) , then ( x − y ) 2 + 3 y 2 is equal to _____.

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MathematicsInverse Trigonometric FunctionsSum And Difference Of AnglesMedium2 minPYQ_2025

MathematicsMediuminteger

If $y = cos (\frac{π}{3} + cos^{- 1} \frac{x}{2})$ , then $(x - y)^{2} + 3 y^{2}$ is equal to _____.

Answer:

Solution:

$y = cos (cos^{- 1} \frac{1}{2} + cos^{- 1} \frac{x}{2}) y = \frac{1}{2} \times \frac{x}{2} - 1 - \frac{1}{4} 1 - \frac{x ^{2}}{4} 4 y = x - 3 4 - x^{2} 3 (4 - x^{2}) = x^{2} + 16 y^{2} - 8 x y 12 - 3 x^{2} = x^{2} + 16 y^{2} - 8 x y 4 x^{2} + 16 y^{2} - 8 x y = 12 x^{2} + 4 y^{2} - 2 x y = 3 x^{2} + y^{2} - 2 x y - 3 y^{2} = 3 (x - y)^{2} + 3 y^{2} = 3$

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

⏱ 2mℹ️ Source: PYQ_2025

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