Question

Differentiate it - Sin x ,cos x ,tan x​

Answer 1

$\huge \pink{answer : }$

(d-dx) sin(x) = lim(d->0) ( sin(x+d) - sin(x) ) / d

= lim ( sin(x)cos(d) + cos(x)sin(d) - sin(x) ) / d

= lim ( sin(x)cos(d) - sin(x) )/d + lim cos(x)sin(d)/d

= sin(x) lim ( cos(d) - 1 )/d + cos(x) lim sin(d)/d

= sin(x) lim ( (cos(d)-1)(cos(d)+1) ) / ( d(cos(d)+1) ) + cos(x) lim sin(d)/d

= sin(x) lim ( cos^2(d)-1 ) / ( d(cos(d)+1 ) + cos(x) lim sin(d)/d

= sin(x) lim -sin^2(d) / ( d(cos(d) + 1) + cos(x) lim sin(d)/d

= sin(x) lim (-sin(d)) * lim sin(d)/d * lim 1/(cos(d)+1) + cos(x) lim sin(d)/d

= sin(x) * 0 * 1 * 1/2 + cos(x) * 1 = cos(x)