Question

simplify into a single fraction and write your answer in terms of sin x and cos x: tan x + 1/tan x

Answer 1

Hint: tanx=sinx/cosx, so 1/tanx=cosx/sinx.
You now only need to write the sum of these as one fraction!

Answer 2

so sin^2x + Cos^2x/cosxsinx ?

Answer 3

anyone?

Answer 4

yes - that is correct but you can simplify this further.\[\sin^2(x)+\cos^2(x)=?\]

Answer 5

o um (sinx)(sinx) + (cosx)(cosx)/cosxsinx

Answer 6

no, the equation I wrote up there is a well know trig identity - look it up in your notes, you must have been taught this at some stage.

Answer 7

1

Answer 8

Pythagorean trig identity

Answer 9

correct

Answer 10

so now make use of that fact to simplify your expression

Answer 11

hmmm

Answer 12

ya idk, I just kinda put it out sin^2x + Cos^2x/cosxsinx = 1 im not seeing how this relates it just made it worse,.

Answer 13

the identity you need to use is:\[\sin^2(x)+\cos^2(x)=1\]

Answer 14

what do u mean, this has nothing to do with this problem lol I mean all I know is that is the Pythagorean tri identity and that you can move cos or sin and lets say u move sin it goes to the right and u have cos^2(x) = plus or minus radical 1-sin^2(x)

Answer 15

Look at the steps you took in this problem:\[\begin{align}
\tan(x)+\frac{1}{\tan(x)}&=\frac{\sin(x)}{\cos(x)}+\frac{\cos(x)}{\sin(x)}\\
&=\frac{\sin^2(x)+\cos^2(x)}{\cos(x)\sin(x)}
\end{align}\]now notice that the numerator contains the terms: \(\sin^2(x)+\cos^2(x)\), and you know that this identity always equals 1. Therefore you can replace \(\sin^2(x)+\cos^2(x)\) by 1.