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