If x=a -b and d^2x dt^2 = then find the value of .

Show that the following point are coplanar:
(0, -1, 0), (2, 1, -1), (1, 1, 1) and (3, 3, 0)

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$\int \frac{\sin x}{\sin 3 x} d x$

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Evaluate the following integrals:$\int\frac{\text{x}}{\sqrt{\text{x}^4+\text{a}^4}}\text{ dx}$

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If $y = x +\tan x$, show that $\cos ^2 x \cdot \frac{d^2 y}{d x^2}-2 y+2 x=0$

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Find $\frac{d y}{d x}$ if : $x^5+x y^3+x^2 y+y^4=4$

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Prove that $f(x) = ax + b$, where $a, b$ are constants and $a < 0$ is an decreasing function on $R$.

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Find the approximate values of:

$\sin \left(29^{\circ} 30^{\circ}\right)$, given that $1^{\circ}=0.0175^{\circ}, \sqrt{ } 3=1.732$.

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If $\text{y}=(\tan^{-1}\text{x})^2$ then prove that $(1+\text{x}^2)\text{y}_2+2\text{x}(1+\text{x}^2)\text{y}_1=2$

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Evaluate the following integrals:
$\int\frac{1}{\text{x}^2}\cos^2\Big(\frac{1}{\text{x}}\Big)\text{dx}$

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Write the value of $\cos^2\Big(\frac{1}{2}\cos^{-1}\frac{3}{5}\Big).$

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Answer