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