# Thread: Need help with trig identities

1. ## Need help with trig identities

If you could go step by step it would be helpful!

cotx+tanx = secxcscx

sin^4x - cos^4x = 2sin^2x - 1

cot^2x-1/1+cot^2x = 1-2sin^2x
Thanks!

2. Originally Posted by Thatoneguy12345
cot^2x-1/1+cot^2x = 1-2sin^2
$\frac{cot^2(x)-1}{cot^2(x)+1}$
$\frac{cot^2(x)-1+1-1}{cot^2(x)+1}$
$\frac{cot^2(x)+1-2}{cot^2(x)+1}$
$\frac{cot^2(x)+1}{cot^2(x)+1}+\frac{-2}{cot^2(x)+1}$
$1+\frac{-2}{cot^2(x)+1}$
$1+\frac{-2}{csc^2(x)}$
$1-2sin^2(x)$

3. Wait, how do you get the -1+1-1 on the 2nd step?

4. Originally Posted by Thatoneguy12345
Wait, how do you get the -1+1-1 on the 2nd step?
1-1 is zero right? If you add it to the equation it doesn't change the value of the equation. But you can use it to simplify the equation, like I did.

For example if you have the equation

5+2 = 7

That's the same as

5+2+(1-1)=7

5. Oh whoa, thanks! Never knew you could do it that way!

6. Q1
Write LHS in terms of sin and cos
Get a common denominator and add
You should recognise and simplify the top
Split up the product
You should now have the RHS
TRY IT!!

Q2 Hint: a^4 - b^4 =(a^2 + b^2)(a^2 - b^2)
The first bracket will be =1
Look at the RHS (there is no cos in sight!)
So, replace (cos x)^2 with 1 - (sin x)^2
Too easy!

Q3 Use the identity 1 + (cot x)^2 = (cosec x)^2 on the bottom
Dividing by (cosec x)^2 is the same as multiplying by (sin x)^2
So now you should have (sin x)^2 x ((cot x)^2 -1)
Write cot^2 in terms of sin and cos
Expand out bracket
Do the same thing you did at the end of Q2 to get rid of cos^2
Done

7. Originally Posted by Thatoneguy12345
cotx+tanx = secxcscx
$cot(x)+tan(x)=sec(x)csc(x)$
$\frac{cos(x)}{sin(x)}+\frac{sin(x)}{cos(x)}$
You choose the common denominator of $cos(x)sin(x)$ and multiply through. You get:
$\frac{cos^2(x)+sin^2(x)}{sin(x)cos(x)}$
Use the identity $sin^2(x)+cos^2(x)=1$
$\frac{1}{sin(x)cos(x)}$
$\frac{1}{sin(x)}*\frac{1}{cos(x)}$
$csc(x)sec(x)$

Edit: If you still need me to show you the second one after Debsta explained it, post the request. Debsta did a good job of explaining it.

8. My thoughts exactly!

9. Thanks a lot you two!