If sin y = x sin (a + y), prove that dy dx = sin^ 2 (a+y) sin a . - Vidyadip

Question

If sin y = x sin (a + y), prove that $\frac{\text{dy}}{\text{dx}}=\frac{\text{sin}^{2}\text{(a+y)}}{\text{sin a}}$.

✓

Answer

sin y = x sin (a + y) $\Rightarrow$ cos y $\frac{\text{dy}}{\text{dx}}$ = x cos (a + y) $\frac{\text{dy}}{\text{dx}}$ + sin (a + y)
$\therefore\frac{\text{dy}}{\text{dx}}= \frac{\text{sin (a + y)}}{\text{cos y - x cos (a + y)}}$
$\text{x} = \frac{\text{sin y}}{\text{sin (a+y)}}\Rightarrow \frac{\text{dy}}{\text{dx}}=\frac{\text{sin (a+y)}}{\text{cos y -}\frac{\text{sin y}}{\text{sin (a+y)}}.\text{cos (a+y)}}$
$\therefore \frac{\text{dy}}{\text{dx}}= \frac{\text{sin}^{2}\text{(a+y)}}{\text{sin (a+y) cos y - cos (a + y) sin y}} = \frac{\text{sin}^{2}\text{(a + y)}}{\text{sin a}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Show that the plane whose vector equation is $\vec{\text{r}}\cdot(\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}})=3$ contains the line whose vector equation is $\vec{\text{r}}=\hat{\text{i}}+\hat{\text{j}}+\lambda(2\hat{\text{i}}+\hat{\text{j}}+4\hat{\text{k}}).$

Evaluate the following integrals:
$\int\limits^{{\pi}}_{{-\pi}}\frac{2\text{x}(1+\sin\text{x})}{1+\cos^2\text{x}}\text{ dx}$

Show that $\int_0^a {f(x)g(x)dx = 2\int_0^a {f(x)dx} } $. If f and g are defined, $f(x) = f(a - x)$ and $g(x) + g(a - x) = 4$

Show that $\text{y}=\text{ae}^{2\text{x}}+\text{be}^{-\text{x}}$ is a solution of the differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\frac{\text{dy}}{\text{dx}}-2\text{y}=0$

Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.

If R is the largest equivalence relation on a set A and S is any relation on A, then:

$\text{R}\subset\text{S}$
$\text{S}\subset\text{R}$
$\text{R = S}$
None of these.

Evaluate the following integrals:
$\int^\limits{(\pi)^\frac{2}{3}}_{0}\sqrt{\text{x}}\cos^2\text{x}^{\frac{3}{2}}\text{ dx}$

On Z, the set of all integers, a binary operation * is defined by a * b = a + 3b - 4. Prove that * is neither commutative nor associative on Z.

Prove that: $\begin{vmatrix}\text{a}&\text{a}+\text{b}&\text{a}+2\text{b} \\\text{a}+2\text{b}&\text{a}&\text{a}+\text{b}\\\text{a}+\text{b}&\text{a}+2\text{b}&\text{a} \end{vmatrix}=9(\text{a}+\text{b})\text{b}^2$

Show that the following curves intersect orthogonally at the indicated points: $x^2 = 4y$ and $4y + x^2 = 8$ at $(2, 1)$