Solution : Since by deleting a single term from an infinite series, it remains same. Therefore, the given function may be written as y = $$\sqrt{sin x + y}$$ Squaring on both sides, $$\implies$$  $$y^2$$  = sin x + y By using differentiation of infinite series, Differentiating both sides with respect to x, 2y $$dy\over … ## Find \(dy\over dx$$ where x = a{cos t + $${1\over 2} log tan^2 {t\over 2}$$} and y = a sin t

Solution : We have, x = a{cos t + $${1\over 2} log tan^2 {t\over 2}$$} and y = a sin t $$\implies$$ x = a{cos t + $${1\over 2} \times 2 log tan{t\over 2}$$} and y = a sin t $$\implies$$ x = a{cos t + {$$log tan{t\over 2}$$} and y = a sin t …

## What is the integration of $$e^x$$ ?

Solution : The integration of $$e^x$$ with respect to x is $$e^x$$ + C. Since $$d\over dx$$ $$e^x$$ = $$e^x$$ dx On integrating both sides, we get $$\int$$ $$e^x$$ dx = $$e^x$$ Hence, the integration of $$e^x$$ is $$e^x$$ + C

## Find the determinant of A = $$\begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{bmatrix}$$.

Solution : | A | = $$\begin{vmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{vmatrix}$$ By using 3×3 determinant formula, $$\implies$$ | A | = $$3\begin{vmatrix} 2 & 1 \\ 1 & -1 \end{vmatrix}$$ – $$(-2)\begin{vmatrix} 1 & 1 \\ 0 & -1 \end{vmatrix}$$ + …

## Find the determinant of $$\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}$$.

Solution : Let | A | = $$\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}$$ By using 2×2 determinant formula, we obtain | A | = ( $$sin^2x$$) – ($$-cos^2x$$) = $$sin^2x$$ + $$cos^2x$$ = 1

## What are the Intercepts cut by the circle on axes ?

Solution : The intercepts cut by the circle $$x^2 + y^2 + 2gx + 2fy + c$$ = 0 on : (i)  x-axis = 2$$\sqrt{g^2 – c}$$ (ii)  y-axis = 2$$\sqrt{f^2 – c}$$ Similar Questions What is the equation of pair of tangents to a circle ? What is the length of tangent to a …

## What is the equation of pair of tangents to a circle ?

Solution : Let the equation of circle S = $$x^2$$ + $$y^2$$ = $$a^2$$ and P($$x_1,y_1$$) is any point outside the circle. From the point we can draw two real and distinct tangent and combine equation of pair of tangents is – ($$x^2$$ + $$y^2$$ – $$a^2$$)($${x_1}^2$$ + $${y_1}^2$$ – $$a^2$$) = \(({xx_1 + yy_1 …