Question

y=tan-¹√1- cos2x/1+cosx find Dy/DX​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\sf{y=tan^{-1}\sqrt{ \dfrac{ 1-cos(2x)}{1+cos(2x) }}}$

$\sf{\implies\,y=tan^{-1}\sqrt{ \dfrac{2sin^{2}(x)}{2cos^{2}(x) }}}$

$\sf{\implies\,y=tan^{-1}\sqrt{ \dfrac{sin^{2}(x)}{cos^{2}(x) }}}$

$\sf{\implies\,y=tan^{-1}\sqrt{ tan^{2}(x)}}$

$\sf{\implies\,y=tan^{-1}(tan(x))}$

$\sf{\implies\,y=x}$

Differentiating both sides, w.r.t x, we get,

$\sf{\blue{\implies\,\dfrac{dy}{dx}=1}}$