# Trigonometry: Prove the Identity

• Oct 27th 2008, 12:38 PM
looi76
Trigonometry: Prove the Identity
$\sin\theta\sec\theta\cot\theta \equiv 1$

$\d{L}\d{H}\d{S} = \sin\theta\sec\theta\cot\theta$

$= \sin\theta \times \frac{1}{\cos\theta} \times \frac{\cos\theta}{\sin\theta}$

After this step I donno what to do. I should proved that $sin\theta\sec\theta\cot\theta$ is equal to $1$, can anyone please help me!

• Oct 27th 2008, 12:43 PM
Moo
Hello !

Long time no see ! :)
Quote:

Originally Posted by looi76
$\sin\theta\sec\theta\cot\theta \equiv 1$

$\d{L}\d{H}\d{S} = \sin\theta\sec\theta\cot\theta$

$= \sin\theta \times \frac{1}{\cos\theta} \times \frac{\cos\theta}{\sin\theta}$

After this step I donno what to do. I should proved that $sin\theta\sec\theta\cot\theta$ is equal to $1$, can anyone please help me!

Well, you're near to it (Surprised)

$\sin\theta \times \frac{1}{\cos\theta} \times \frac{\cos\theta}{\sin\theta}=\sin \theta \times \frac{1}{\cos \theta} \times \cos \theta \times \frac{1}{\sin \theta}$

Group it : $=\sin \theta \times \frac{1}{\sin \theta} \times \cos \theta \times \frac{1}{\cos \theta}$

doesn't it simplify ? :o
• Oct 27th 2008, 12:50 PM
looi76
Quote:

Originally Posted by Moo
Hello !

Long time no see ! :)

Well, you're near to it (Surprised)

$\sin\theta \times \frac{1}{\cos\theta} \times \frac{\cos\theta}{\sin\theta}=\sin \theta \times \frac{1}{\cos \theta} \times \cos \theta \times \frac{1}{\sin \theta}$

Group it : $=\sin \theta \times \frac{1}{\sin \theta} \times \cos \theta \times \frac{1}{\cos \theta}$

doesn't it simplify ? :o

Thanks for making it CLEAR!(Nod)

You remember me (Rofl), Now, I'm in the University!