# Thread: Quick and easy question trig identities

1. ## Quick and easy question trig identities

Hey, I am just starting my trig identities unit and I have a question I'm stuck on.. it's probably very easy, so bear with me and don't make fun of me ^^

(sec˛x + csc ˛x) - (tan˛x - cot˛x)
So I have ( 1/cos˛x+ 1/sin˛x) - (sin˛x/cos˛x+ cos˛x/sin˛x)...

2. Originally Posted by Slipery
Hey, I am just starting my trig identities unit and I have a question I'm stuck on.. it's probably very easy, so bear with me and don't make fun of me ^^

(sec˛x + csc ˛x) - (tan˛x - cot˛x)
So I have ( 1/cos˛x+ 1/sin˛x) - (sin˛x/cos˛x+ cos˛x/sin˛x)...
i suppose you want to simplify here? that's good. now just combined the fractions in each set of brackets. then combine the two resulting fractions

3. Yes, just simplify.

For the first bracket, (1/cos˛x + 1/sin˛x)
can I change the cos˛x and sin˛x to 1 and have it as 1+1= 2?

4. Hello, Slipery!

Your work is correct, but are you aware of these identities?

. . . $\begin{array}{ccc}\sec^2\!x \:=\:\tan^2\!x + 1 & \Rightarrow & \sec^2\!x - \tan^2\!x \:=\:1 \\
\csc^2\!x \:=\:\cot^2\!x + 1 & \Rightarrow & \csc^2\!x - \cot^2\!x \:=\:1\end{array}$

Simplify: . $(\sec^2\!x + \csc^2\!x) - (\tan^2\!x + \cot^2\!x)$

We have: . $(\sec^2\!x - \tan^2\!x) + (\csc^2\!x - \cot^2\!x) \;\;=\;\;1 + 1 \;\;=\;\;2$

5. Ahhh, that is very helpful. thank you both soroban and jhevon.
I honestly think my brain has issues with this type of work, it just wont' draw the connections.