The equation you provided is:

$\frac{\csc(\theta) \cdot \tan(\theta)}{\sec(\theta)} = 1$

Simplification Steps:

1. Use the trigonometric identities:

   • $\csc(\theta) = \frac{1}{\sin(\theta)}$
   • $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$
   • $\sec(\theta) = \frac{1}{\cos(\theta)}$

2. Substitute these identities into the equation: $\frac{\left(\frac{1}{\sin(\theta)}\right) \cdot \left(\frac{\sin(\theta)}{\cos(\theta)}\right)}{\frac{1}{\cos(\theta)}} = 1$

3. Simplify the numerator: The $\sin(\theta)$ terms cancel out in the numerator: $\frac{1}{\cos(\theta)} \cdot \cos(\theta)$

4. Simplify further: The $\cos(\theta)$ terms also cancel out, leaving: $1 = 1$

Thus, the equation simplifies to $1 = 1$, which is an identity and always true.

Would you like any further details or have any questions?

Related Questions:

1. How do you derive the trigonometric identities for $\csc(\theta)$ and $\sec(\theta)$?
2. Why is $1 = 1$ considered a trigonometric identity?
3. Can this identity be useful in solving other trigonometric equations?
4. What are the reciprocal identities of other trigonometric functions?
5. How would this equation change if it involved a different trigonometric function, such as $\cot(\theta)$?

Tip:

Always remember to use fundamental trigonometric identities when simplifying complex trigonometric expressions.