$\cos 45°.\sec 45°=$

Let's begin with the given expression: cos 45° × sec 45°.

Step-by-Step Solution:

1. We know that the cosine of 45° is:

   cos 45° = 1 / √2

2. Similarly, secant is the reciprocal of cosine. Hence:

   sec 45° = 1 / cos 45° = √2

3. Now, substituting these values into the given expression:

   cos 45° × sec 45° = (1 / √2) × √2

4. On simplifying, the result is:

   cos 45° × sec 45° = 1

Additional Examples

Example 1: sin 45° × cos 45°

We know that sin 45° = cos 45° = 1 / √2.

So, the expression sin 45° × cos 45° is: sin 45° × cos 45° = (1 / √2) × (1 / √2) = 1/2.

Example 2: sin 60° × sec 60°

We know that sin 60° = √3 / 2 and sec 60° = 2 / √3.

The expression sin 60° × sec 60° is: sin 60° × sec 60° = (√3 / 2) × (2 / √3) = 1.

Conclusion

In this example, cos 45° × sec 45° evaluates to 1. Understanding the relationship between cosine and secant helps simplify such calculations easily. Keep practicing similar problems to gain more clarity on trigonometric functions and their properties!