# Thread: Trigonometry: Prove the Identity

1. ## Trigonometry: Prove the Identity

$\displaystyle \sin\theta\sec\theta\cot\theta \equiv 1$

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

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

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

2. Hello !

Long time no see !
Originally Posted by looi76
$\displaystyle \sin\theta\sec\theta\cot\theta \equiv 1$

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

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

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

Well, you're near to it

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

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

doesn't it simplify ?

3. Originally Posted by Moo
Hello !

Long time no see !

Well, you're near to it

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

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

doesn't it simplify ?
Thanks for making it CLEAR!

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