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don't know how my calc books did this(deriv of trig)

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*this is not homework* My calculus book is proving the derivatives of trigonometric functions to me. At one point it changes an inequality into another form, and I dont' understand how it did it at all. It goes like this. x < tan x = x < (sin x)/(cos x) = cos x < sin x/x Thats it. I have no clue how it did that. I understand the tan to sin/cos part, but not the third part. Can anyone proof this works? I know there's some math buffs who love this stuff. Thanks so much :]

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as far as my limited math knowledge.

they multiply both sides by cos x

giving

x ( cos x ) / ( sin x )

then divide by x giving

( cos x ) < ( sin x ) / x

least thats what i think is happening ... can any math geniuses confirm this or show how little math i really know :)

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Quote:
Original post by xorjesus
x < (sin x)/(cos x)
=
cos x < sin x/x

you just multiply both sides of the equation by (cos x) then divide by x.
you can write it split like that:
x<(sin x)/(cos x)
=
x (cos x)<(sin x)
=
cos x< (sin x)/x

//edit:beaten by 12 seconds :]

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Guest Anonymous Poster
And it's only valid if you multiply /divide by a positive number, else you've to change the inequality sign, '' and vice versa.

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