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If , then prove that .

Mathematics20204 marksDerivation
If $\cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \theta$, then prove that $9x^2 - 12xy\cos\theta + 4y^2 = 36\sin^2\theta$.

Given: $\cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \theta$

To show: $9x^2 - 12xy\cos\theta + 4y^2 = 36\sin^2\theta$

Answer

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Inverse Trigonometric Functions

From ISC 2020 Mathematics Paper 1, question 3(a).