# Thread: Trig/Proving Identities

1. ## Trig/Proving Identities

I'm completely stumped. were supposed to prove the equations true. if you could help me that would be great!

3.) sec^2(θ)-sec^2(θ)sin^2(θ)=1

4.) sec^2(θ)cot^2(θ)-1=cot^2(θ)

5.) 1/sec(θ)-cos(θ)=cot(θ)csc(θ)

6.) sec^2(θ)+csc^2(θ)=csc^2(θ)sec^2(θ)

7.) [1/sin(θ)+1] - [1/sin(θ)-1]=2sec^2(θ)

8.) [sin(θ)tan(θ]/[1-cos(θ)]=sec(θ)=1

2. #1: It often helps to rewrite it in terms to sine and cosine.

$sec^{2}(x)-sec^{2}(x)sin^{2}(x)$

$=\frac{1}{cos^{2}(x)}-\frac{sin^{2}(x)}{cos^{2}(x)}$

$=\frac{1-sin^{2}(x)}{cos^{2}(x)}$

$=\frac{cos^{2}(x)}{cos^{2}(x)}=1$