Question

if y = √1+cos 2X /√1-cos 2X ,find dy/dx.

Answer 1

$\textbf{Given:}$

$\mathsf{y=\dfrac{\sqrt{1+cos\,2x}}{\sqrt{1-cos\,2x}}}$

$\textbf{To find:}$

$\mathsf{\dfrac{dy}{dx}}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{y=\dfrac{\sqrt{1+cos\,2x}}{\sqrt{1-cos\,2x}}}$

$\mathsf{Using,}$

$\boxed{\mathsf{cos2x=1-2\,sin^2x\;\implies\;1-cos2x=2\,sin^2x}}$

$\boxed{\mathsf{cos2x=2\,cos^2x-1\;\implies\;1+cos2x=2\,cos^2x}}$

$\mathsf{y=\dfrac{\sqrt{2\,cos^2x}}{\sqrt{2\,sin^2x}}}$

$\mathsf{y=\dfrac{\sqrt{2}\,cosx}{\sqrt{2}\,sinx}}}$

$\mathsf{y=\dfrac{cosx}{sinx}}$

$\mathsf{y=cotx}$

$\textsf{Differentiate with respect to 'x'}$

$\boxed{\mathsf{\dfrac{dy}{dx}=-cosec^2x}}$

$\textbf{Find more:}$

If y=e^2x (ax+b), then prove that d^2 y/dx^2 -4 dy/dx+4y=0

https://brainly.in/question/19674230

Answer 2

Step-by-step explanation:

see the above picture..............