Question

what is the differentiation of sin x​

Answer 1

ANSWER:-

The differentiation of sin x = cos x.

Differentiation of sin x using First Principle :-

We have,

lim h-0 sin(x+h) - sin x / h

lim h-0 2cos { (x+x+h) / 2).sin (x+h-x) / 2) } / h

lim h-0 { 2cos (x+h/2).sin [ (h/ 2) / (h/2) ]*h / 2} / h

That is,

sinx / x = 1

2cosx / 2

Cancelling 2 from both numerator and denominator, we get,

= cosx.

Answer 2

Answer :-

THE DERIVATIVE of sin x is cos x. To prove that, we will use the following identity: sin A − sin B = 2 cos ½(A + B) sin ½(A − B).