write in terms of sin and cos

the problem asks me to write sec - tan x sin in terms of sin and cos and the answer in the book is just cos. im assuming they want me to use some identities and then find the lcd and simplify but i haven't been in school for about 6 years and my brain isn't working... please help me see how sec - tan x sin reduces to cos. thanks :)

Re: write in terms of sin and cos

Quote:

Originally Posted by

**sinceredoper** the problem asks me to write sec - tan x sin in terms of sin and cos and the answer in the book is just cos. im assuming they want me to use some identities and then find the lcd and simplify but i haven't been in school for about 6 years and my brain isn't working... please help me see how sec - tan x sin reduces to cos. thanks

$\displaystyle \sec(x)-\tan(x)\sin(x)=\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)}\sin(x)=\frac{1-\sin^2(x)}{\cos(x)}$

Re: write in terms of sin and cos

thats what i had written out but the book is saying the answer is just cos. im reading more and i guess im supposed to use the pythagorean identity for 1 so it's cos^2 + sin^2 - sin^2 / cos, which reduces to cos^2 / cos and then just cos? if thats right please let me know. im 2 days into learning trig after a 6 year break from math. nothing is making sense. lol

thx for quick response.

Re: write in terms of sin and cos

Quote:

Originally Posted by

**sinceredoper** thats what i had written out but the book is saying the answer is just cos. im reading more and i guess im supposed to use the pythagorean identity for 1 so it's cos^2 + sin^2 - sin^2 / cos, which reduces to cos^2 / cos and then just cos? if thats right please let me know. im 2 days into learning trig after a 6 year break from math. nothing is making sense.

$\displaystyle 1-\sin^2(x)=\cos^2(x)$ and is it true that $\displaystyle \frac{C^2}{C}=C~?$

Re: write in terms of sin and cos

i get it now, i went full retard. thanks :)

Re: write in terms of sin and cos

Also note, sin, cos, tan, sec, csc and cot are all MEANINGLESS without a variable attached to them!