Question

x=sinx+cosx y=cosx-sinx. prove that dy/dX +tan(π\4-x)​

Answer 1

${\bold{\huge{\red{\boxed{\green{given}}}}}}$

$x = sina+ cosab - - - (1)$

$y = cosa - sina - - - (2)$

${\bold{\huge{\red{\boxed{\green{To\: prove}}}}}}$

$\frac{dy}{dx} + tan( \frac{ \pi}{4} - x)$

now differentiate equation (1) w.r.t. a

$\frac{dx}{da} = - cos \: a + \: sina$

then diffrentiate equation (2) w.rt. a

$\frac{dy}{da} = - sina - cosa$

now we can say,

$\frac{dy}{dx} = \frac{ - (sina + cosa)}{ -( cosa \: - sin \: a)}$