If x = a , y = b then d y d x = ? - Vidyadip

Question

If $x = a \sec \theta, y = b \tan \theta$ then $\frac{d y}{d x}= ?$

✓

Answer

$x = a \sec \theta$, we get
$\therefore \frac{d x}{d \theta}=\operatorname{asec} \theta \cdot \tan \theta$
$\therefore \frac{d \theta}{d x}=\frac{1}{asec \theta \cdot \tan \theta}$
$y=b \tan \theta \cdot we \text { get }$
$\therefore \frac{d y}{d \theta}=b \cdot \sec ^2 \theta$
$\Rightarrow \frac{d y}{d x}=\frac{d y}{d \theta} \times \frac{d \theta}{d x}$
$\Rightarrow \frac{d y}{d x}=b \cdot \sec ^2 \theta \times \frac{1}{asec \theta \cdot \tan \theta}$
$\Rightarrow \frac{d y}{d x}=\frac{b \sec \theta}{atan \theta}$
$\Rightarrow \frac{dy}{dx}=\frac{b \cdot \frac{1}{\cos \theta}}{a \cdot \frac{\sin \theta}{\cos \theta}}$
$\Rightarrow \frac{d y}{d x}=\frac{b}{a} \operatorname{cosec} \theta $

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 "M.C.Q (1 Marks)" from Model Paper 2→Model Paper 2 — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

In which of the following, function $f(x)=x^2-4 x$ +6 is increasing :

If $f(x)=x^2+4 x-5$ and $A=\left|\begin{array}{ll}1 & 2 \\ 4 & -3\end{array}\right|$, then $f(A)$ is equal to

Which of the following is not true about feasibility?

It cannot be determined in a graphical solution of an LPP.
It is independent of the objective function.
It implies that there must be a convex region satisfying all the constraints.
Extreme points of the convex region gives the optimum solution.

The integrating factor of the differential equation $\left(x+3 y^2\right) \frac{d y}{d x}=y$ is

If one ball is drawn ar random from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, then the probability that 2 white and 1 black balls will be drawn is.

Evaluate $\begin{bmatrix}4&8&12\\6&12&18\\7&14&21\end{bmatrix}$ is:

168
-1
-168
0

If $\int\frac{\sin^8\text{x}-\cos^8\text{x}}{1-2\sin^2\text{x}\cos^2\text{x}}\text{ dx}=\text{a}\sin2\text{x}+\text{C},$ then a =

$-\frac{1}{2}$
$\frac{1}{2}$
$-1$
$1$

If a relation $R$ is defined on the set $Z$ of integers as follows: $(a, b) \in R \Leftrightarrow a^2 + b^2 = 25$. Then, domain $(R)$ is:

Choose the correct answer from the given four option.
Integrating factor of the differential equation $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\tan\text{x}-\sec\text{x}=0$ is:

$\cos\text{x}$
$\sec\text{x}$
$\text{e}^{\cos\text{x}}$
$\text{e}^{\sec\text{x}}$

The area of region bounded by curve $\text{y}=\cos2\text{x},$ line $\text{x}=0$ $\text{x}=\frac{\pi}{3}$ is:

$\frac{2-\sqrt{3}}{4}$
$\frac{\sqrt{3}}{4}$
$\frac{4-\sqrt{3}}{4}$
$\frac{\sqrt{3}-4}{4}$