i dont know which identiy formula to use to solve tanxcscx

Question

zepdrix · Answer

When you're not sure, it's usually a good idea to try changing everything to sines and cosines and see if anything cancels out.

So we'll have to remember what tanx and cscx are in terms of sines and cosines.
Remember those or no? :)

lindsey11x16 · Answer

cscx can be 1/sinx

zepdrix · Answer

true story :U

zepdrix · Answer

and tangent? :D

lindsey11x16 · Answer

tanx = 1/cotx but i dont know where to go from there n_n

lindsey11x16 · Answer

u_u

zepdrix · Answer

Yes it's true that tan x = 1/cot x, but that doesn't really help us :) We want tangent in terms of sines and cosines. Maybe you'll remember this lil identity.
$$\large \tan x = \frac{\sin x}{\cos x}$$

zepdrix · Answer

$$\huge \tan x \cdot \csc x \qquad \rightarrow \qquad \frac{\sin x}{\cos x}\cdot \frac{1}{\sin x}$$Make sense? :O See any nice cancellations? :D

lindsey11x16 · Answer

Lol wow that was such a big help

how do you see cancellations so easily? like this is really hard

zepdrix · Answer

These can be pretty tricky, you have sooooo many identities to remember in trig.

You want to be able to get to a point where you just look at something and your brain goes, "oh that looks like this idenity, let's try something"

If you're totally lost on a problem, converting to sines and cosines is a really good first step, sometimes it helps :)

Ok do you understand the last step of this problem? It's a good idea to rewrite your final answer as a single trig function, instead of the ugly fraction.

zepdrix · Answer

It looks like we have a nice cancellation with the sines, leaving us with...$$\huge \frac{1}{\cos x}$$Do you remember an identity for this one? :)

lindsey11x16 · Answer

i'm working on memorizing them ! 

and 1/cosx is equal to secant x

lindsey11x16 · Answer

?

zepdrix · Answer

yay team \:D/

lindsey11x16 · Answer

omg thank you!

lindsey11x16 · Answer

at first i thought the answer would be 1/cosx , how do i know if i'm supposed to keep going or i can leave it at 1/cosx 

thats what i thought was hard :/

zepdrix · Answer

Well you have 1 trig term, that's a good indicator that you're done.
We were able to simplify it down to one of the 6 trig functions, but if you had left it as 1/cos x that's not a big deal.

We started with 2 trig functions, and we were able to simplify them down to a single trig function. That's usually a good identifier that you've done most if not all of the work that you needed to do.