Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

show that xcosec^2x = cotx - d/dx xcotx

Show That Xcosec2x Cotx Ddx Xcotx class=

Sagot :

The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

Learn more about differentials at

https://brainly.com/question/14830750

#SPJ1