Hello Aspirant,

I hope that you are doing well.

f(x)= log sin(x)

f(x+h)= log sin (x+h)

f(x+h)= f(x) + h f'(x) + h^2/2! f"(x)+ h^3/3! f'''(x)+...

f(x)= log(sin x)

f'(x)= cos x/ sin x=cot x

f"(x) = -cosec^2 x

f"'(x) = 2 cosec^2 cot x

log sin(x+h) = log(sin x) + h cot x - h^2 cosec^2 /2+

h^3/3 cosec^2x cot x + .........

I hope this helps.

Good luck!

Thank you