while finding the derivative of an equation is it necessary to convert it into the trigonometric form.For Ex:  ?

It is a trigonometric identity: sin(2x) = 2 sin(x) cos(x)

When you get an answer of 4 sin(x) cos(x), you may convert it into 2 sin(2x) but not must. Usually, I do it.

4sinxcosx can be differentiated using the product rule, or we can convert to 2sin2x and differentiate.

However, when integrating, it is a lot easier to integrate a function bsin(ax) than it is a product.

You can use 'integration by parts' but, this can lead to many steps of working.

:)>

Sin(2x) = Sin( x + x) 
then by the Trig. Identity 
Sin(x + x) = SinxCosX + CosX Sinx = 
2SinxCosx 
Let y= 2SinxCosx 
Then differentiate by Product Rule 
Hence dy.dx = 2Sinx(-Sinx) + 2CosxCosx
dy/dx = -2Sin^2(x0 + 2Cos^2(x) 
Remember the Trig Identity 
Cos^2 = 1 - Sin^ 
Hence 
dy/dx = -2Sin^2(x) +2(1 - Sin^2(x))
dy/dx = -2Sin^2(x) + 2 - 2Sin^2(x) 
dy/dx = 2 - 4Sin^2(x)