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SugarRainbow
 3 years ago
simplify tan x cos x
SugarRainbow
 3 years ago
simplify tan x cos x

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qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1Remember tangent is just sin(x)/cos(x)

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0so its cos x (sin x / cos x) ?

qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1Correct, now what happens when you go ahead and multiply the cosine?

qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1That's it. The cosines cancel.

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0okay cool what bout sec y sin (pi/2y)? IDK how to do this at all

qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1\[\sec(y)\sin(\frac{\pi}{2y})\] ??

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0but isnt it like pi/2  y not pi/ 2y

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1sin(pi/2y)=cos y sec y= 1/cos y

qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1Ok, so rewrite secant as 1/cos

qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1Then you can use a fancy pants trig identity.

qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1347861835303:dw Right?

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0i think so i was kinda looking at what hartnns post too so couldn't you do it likedw:1347861948541:dw

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1sec y =1/ cos y is in numerator, so it would be :dw:1347862109049:dw

qpHalcy0n
 3 years ago
Best ResponseYou've already chosen the best response.1No, well what you would have is a multiplication, the cosines would cancel.

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh hey you know how tan x= sinx/ cos x well what are the rest of those cuz it might help me understand better like how we getting cos y when its sin y

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1ok, so u want all trignometric formulas ? for converting one ratio to other ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1i will list some : \(\huge sin x =1/cosec x \implies cosec x=1/sin x \\\huge cos x = 1/sec x \implies secx=1/cos x \\\huge tan x=1/cot x \implies cot x =1/tanx \\\huge tan x=sin x/cos x \\\huge cot x=cos x/sinx \\ \huge sin^2x+cos^2x=1 \\\huge sec^2x=1+tan^2x\\\huge cosec^2x=1+cot^2x\)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1if u want sin x when cos x is given or if u want cos x when sin x is given, u use: \(sin^2x+cos^2x=1\)

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0so if its 1+tan^2x/csc^2x that would simplify to sec^2x/csc^2

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1yes. or is it ? \(\large1+\frac{tan^2x}{cosec^2x}\quad?\)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1if it is \(\large\frac{1+tan^2x}{cosec^2x}=\frac{sec^2x}{cosec^2x}=\frac{sin^2x}{cos^2x}=tan^2x\)

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0but you put that cos^2x=1+cot^2x

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1no the last one is cosec^2 x =1+cot^2 x not cos^2x=1+cot^2x

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah huh cosec is csc not cos i forgot for a minute lol

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0so is it 1+ tan^2x/csc^2x or sec^2x/csc^2 and why

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1what exactly is your question ? is this : (1+ tan^2x)/csc^2x

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1(1+ tan^2x)=sec^2 x from the formula i gave u.

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0no i saying is it my answer or yours and why (idk how to put it on my computer like you did so that was the best i could do)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1to tell u what is your answer, i need to know your exact question, that is why i asked whether it is: (1+ tan^2x)/csc^2x

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah it's that and i need to simplify it

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1ok,for that i have shown u the steps, tell me which step, u didn't understand: \(\large\frac{1+tan^2x}{cosec^2x}=\frac{sec^2x}{cosec^2x}=\frac{sin^2x}{cos^2x}=tan^2x\)

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh i get it now earlier you put it wierd so i didn't get it

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0okay now this one is cot x tan x so it would be (cosx/sinx)(sinx/cosx) correct?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1yes, or u could use cot x = 1/ tanx and u get tan x / tan x =1

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0wait because i have two of each would thay cancel out?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1yes, they would. sin x cos x / sin x cos x =1

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh okay just checking

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0how bout cot u sin u would that simplify to (cosu/sinu)sin u= cos u?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1thats absolutely correct! u are improving :)

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0hooray improvement!

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.01cos^2 beta/sin beta and that would simplify to ooh okay i got nothin for this one :(

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1is the numerator (1cos^2 beta ) ??

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1from sin^2 beta +cos^2 beta =1 u have 1cos^2 beta = sin^2 beta so u have : \(\large \frac{sin^2 \beta}{sin \beta}=\frac{sin \beta.sin\beta}{sin \beta}=?\)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1yup, but did u get all steps ?

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0yeah so is that another function 1cos^2 beta = sin^2 beta

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1see the list i have given. it has sin^2 x + cos^2 x =1 isn't it ? from here i got 1cos^2 x = sin^2 x clear ?

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh so you just went backwards?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1whenever u see sin^2 x or cos^2 x try to use that formula for simplification.

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0okay now i have cos x cos^3 x

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0like would that be cosx (cosx)(cosx)/cosx?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1nopes. take cos x common from both the terms, what do u get ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1cosx (cosx)(cosx)(cosx)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1no! after taking cos x common, u get cos x (1(cos x)(cos x) ) =cos x (1 cos^2 x) and u already know what is (1 cos^2 x)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1yes! so your final answer will be cos x sin^2x but did u get all the steps ?

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0yeah because you have coxx(cosx)(cosx)(cosx) =cosx1(cosx)=1cos^2x=sin^2x

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1i will draw it :dw:1347866550463:dw

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh okay then now my last question is sin^2 u + tan^2 u +cos^2 u/sec u

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1is this entire thing (sin^2 u + tan^2 u +cos^2 u) in the numerator ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1again using sin^2 x +cos^2 x =1, u have numerator as (1+tan^2 x) got this ? and (1+tan^2 x) = sec^2 x.....see formula list. so u have now sec^2x/sec x = ??

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1replace all of my 'x' with 'u'

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah so now you have sec x!

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah lol thanks for your help i going to sleep now so goodnight^^

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1a very good night to u and have sweet dreams :)
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