The solution of tan y frac{dy}{dx} = sin(x+y) | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given: $	an y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$Using the trigonometric identity $\sin C + \sin D = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})

Vedclass · Accepted Answer

$\sec y = -2 \cos x + c$

Vedclass · Answer

(B) Given: $	an y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$Using the trigonometric identity $\sin C + \sin D = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})$:$	an y \frac{dy}{dx} = 2 \sin x \cos y$Rearranging the terms to separate variables:$\frac{\sin y}{\cos^2 y} dy = 2 \sin x dx$Integrating both sides:$\int \frac{\sin y}{\cos^2 y} dy = \int 2 \sin x dx$Let $t = \cos y$,then $dt = -\sin y dy$,so $\sin y dy = -dt$.Substituting this into the integral:$-\int \frac{dt}{t^2} = -2 \cos x + c$$-(- \frac{1}{t}) = -2 \cos x + c$$\frac{1}{\cos y} = -2 \cos x + c$$\sec y = -2 \cos x + c$

The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is

Similar Questions

When acetaldehyde is reacted with $LiAlH_4$,what is the product formed?

$A$ charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to:

Which of the following is an example of a Gram-negative bacterium?

Which of the following statements are correct?
$(i)$. Genus comprises a group of related species.
$(ii)$. Taxon represents a taxonomic group of individual organisms.
$(iii)$. Family comprises a group of related genera.
$(iv)$. Taxonomic category class includes related orders.

The radioactive sources $A$ and $B$ have half-lives of $2 \ hr$ and $4 \ hr$ respectively and initially contain the same number of radioactive atoms. At the end of $2 \ hr$,the ratio of their rates of disintegration is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module