Prove that ^ –1 ( x 1 + sinx )= 4 -x 2 ,x (- 2 , 2 ).

Find the equation of the plane with intercept 3 on the y-axis and parallel to the ZOX plane.

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Show that the points A (1, 2, 7), B (2, 6, 3) and C(3, 10, -1) are collinear.

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Check the commutativity and associativity of the following binary operations : $'*'$ on $Q$ defined by $a * b = (a - b)^2$ for all $a, b \in Q$.

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If $\text{y}=\cos^{-1}(2\text{x})+2\cos^{-1}\sqrt{1-4\text{x}^2}, 0 <\text{x}<\frac{1}{2},$ find $\frac{\text{dy}}{\text{dx}}.$

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Write the value of $\cos\Big(2\sin^{-1}\frac{1}{3}\Big).$

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Solve for x:
$\tan^{-1} \bigg(\frac{x - 2}{x - 1}\bigg) + \tan^{-1} \bigg(\frac{x + 2}{x + 1}\bigg) = \frac{\pi}{4}$

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Evaluate the following integrals:
$\int\sec^42\text{x}\text{ dx}$

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State with reasons whether the following functions have inverse:
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}

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Using vector method, prove that the point is collinear:
A(1, 2, 7), B(2, 6, 3) and C(3, 10, -1)

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$\int\frac{1}{1+\cos3\text{x}}\text{dx}$

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Answer