Question

Y = x tanx/2
, then (1+ cosx)dy/dx-sin x =
a) xy
b) x
c) 0
d) y

Answer 1

Answer:

b) X

Step-by-step explanation:

Y=xtanx/2

dy/dx=xsec²x/2*1/2+tanx/2

=x/2sec²x/2+tanx/2

Now

(1+cosx)(x/2sec²x/2+tanx/2)-sinx

2cos²x/2(x/2sec²x/2+tanx/2)-sinx

x+2sinx/2cosx/2 - 2sinx/2cosx/2

x

Answer 2

Answer:

(1+ cosx)dy/dx-sin x= x.

Step-by-step explanation:

Given: y = x tanx/2.

To find (1+ cosx)dy/dx-sin x.

Taking y=xtanx/2

Differentiate both sides with respect to x we get:

dy/dx=x[sec²(x/2)]*1/2+tan(x/2)

         =x/2sec²(x/2)+tan(x/2)

Substitute value of dy/dx=x/2sec²(x/2)+tan(x/2) in (1+ cosx)dy/dx-sin x we get:

(1+ cosx)dy/dx-sin x= (1+cosx)(x/2sec²x/2+tanx/2)-sinx

                               = 2cos²x/2(x/2sec²x/2+tanx/2)-sinx

                               = x+2sinx/2cosx/2 - 2sinx/2cosx/2

                               = x

Hence, option b is correct.

#SPJ3