Question

let's if i did this one right
prove that \[|\sin a-\sin b |\leq |b-a|\]

Answer 1

so i will let f(x)=sinx which is differentiable at (a,b)
so then i can use the MVT

Answer 2

HI!!

Answer 3

yes is a straightforward application of the mvt

Answer 4

some \[a<c<b\] such that \[f(b)-f(a)=f'(c)(b-a)\]
abs to it
\[|f(a)-f(b)|=|f'(c)||b-a|\]
\[|\sin a-\sin b |=|\cos c||b-a|\leq |b-a|\]

Answer 5

hey @misty1212 i guess

Answer 6

finished

Answer 7

i guess did i forgot something

Answer 8

let me recheck the question hhee

Answer 9

could find the original Q darn it lol

Answer 10

shoud be |a-b| i actually forgot the take care of the sign for that side as well
\[|\sin a -\sin b|=\cos c|a-b|\leq|a-b|\]
hence proved :)