Question

lf y= tan inverse 1 [cos x/1-sin x] find dy/dx​

Answer 1

Heya!!

Let's simplify this Cos x / (1 - Sin x)

=

Cos² x/2 - Sin² x/2 /( Cos x/2 - Sin x/2 )²

=

Cos x/2 + sin x/2 /( Cos x/2 - Sin x/2 )

=

Cos x/2 { 1 + Tan x/2 }
________________
Cos x/2 { 1 - Tan x/2 }

=

Tan ( 45 + x/2 }

y = Tan-¹ ( Tan ( 45 + x/2 ) )

y = 45 + x/2

Now, Differentiate y w.r.t.x

dy/dx = 1/2